Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology

We begin with some remarks explaining the structure of this article. After some introductory statements in the following paragraphs, we summarize the historic development of what is now often called “Nonsymmetric or Asymmetric Topology” in Section 2. In the following, more specific sections we discuss the historic development of some of the main ideas of the area in greater detail. The list of sections and keywords given above should help the specialist to find his way through the various sections.

[1]  J. Penot,et al.  Infinite products of relations, set-valued series and uniform openness of multifunctions , 1995 .

[2]  Philipp Sünderhauf.  Tensor products and powerspaces in quantitative domain theory , 1997, MFPS.

[3]  P. V. Subrahmanyam,et al.  Cauchy sequences in quasi-pseudo-metric spaces , 1982 .

[4]  R. Kopperman,et al.  Smyth completion as bicompletion , 1999 .

[5]  Philipp Sünderhauf.  Constructing a quasi-uniform function space , 1995 .

[6]  Ralph Kopperman,et al.  Continuity Spaces: Reconciling Domains and Metric Spaces , 1997, Theor. Comput. Sci..

[7]  S. Romaguera.  ALMOST 2-FULLY NORMAL, PAIRWISE PARACOMPACT AND COMPLETE DEVELOPABLE BISPACES , 2001 .

[8]  H. Künzi,et al.  A nontrivial T1-space admitting a unique quasi-proximity , 1996, Glasgow Mathematical Journal.

[9]  W. Pervin,et al.  Completeness in quasi-uniform spaces , 1965 .

[10]  Bernhard Banaschewski,et al.  Stably continuous frames , 1988, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  L. M. Brown.  Semi-sequentially normal bitopological spaces , 1992 .

[12]  K. Porter.  The open-open topology for function spaces , 1993 .

[13]  On a property of pseudometrics and uniformities near to convexity , 1988 .

[14]  R. Lowen,et al.  Approximations in Functional Analysis , 2000 .

[15]  V. Gregori,et al.  On the Hahn-Banach Theorem in Certain Linear Quasi-uniform Structures , 1999 .

[16]  P. Fletcher,et al.  Topological spaces with a unique compatible quasi-uniform structure , 1970 .

[17]  Alexander P. Sostak,et al.  EVEN FUZZY TOPOLOGIES AND RELATED STRUCTURES , 1997 .

[18]  Anna Di Concilio.  Spazi quasimetrici e topologie ad essi associate , 1971 .

[19]  H. Künzi,et al.  Stability in quasi-uniform spaces and the inverse problem , 1993 .

[20]  Worthen Hunsaker,et al.  Completion of Quasi-Uniform Frames , 1999, Appl. Categorical Struct..

[21]  Jan Rutten.  Elements of generalized ultrametric domain theory , 1996 .

[22]  E. P. Lane.  Bitopological Spaces and Quasi‐Uniform Spaces , 1967 .

[23]  R. Hodel.  Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity , 1998 .

[24]  Massood Seyedin.  ₃-quasi-uniform spaces and topological homeomorphism groups , 1975 .

[25]  Krzysztof Ciesielski,et al.  Characterizing Topologies With Bounded Complete Computational Models , 1999, MFPS.

[26]  Klaus Keimel,et al.  Ordered cones and approximation , 1992 .

[27]  R. Engelking,et al.  Paracompactness in ordered spaces , 1977 .

[28]  A. Losonczi.  Finite Quasi-Uniform Extensions. I , 2004 .

[29]  H. Künzi,et al.  The Doitchinov Completion of a Regular Paratopological Group , 1998 .

[30]  L. M. Brown.  P-Q-Metrizability of Bitopological Spaces with a Dual Base of Countable Order , 1999 .

[31]  H. Künzi,et al.  Bicompleteness of the fine quasi-uniformity , 1991, Mathematical Proceedings of the Cambridge Philosophical Society.

[32]  R. Lowen.  Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad , 1997 .

[33]  Hugo Ribeiro,et al.  Sur les espaces à métrique faible , 1943 .

[34]  S. Romaguera,et al.  Bicompleting the left quasi-uniformity of a paratopological group , 1998 .

[35]  Salvador Romaguera,et al.  On bicomplete quasi-pseudometrizability , 1993 .

[36]  Philipp Sünderhauf.  SMYTH COMPLETENESS IN TERMS OF NETS: THE GENERAL CASE , 1997 .

[37]  G. Brümmer.  On the non-unique extension of topological to bitopological properties , 1982 .

[38]  P. Fletcher,et al.  Orthocompactness and strong Čech completeness in Moore spaces , 1972 .

[39]  G. Gruenhage.  A Note on Quasi-Metrizability , 1977, Canadian Journal of Mathematics.

[40]  A. K. Katsaras.  Fuzzy quasi-proximities and fuzzy quasi-uniformities , 1988 .

[41]  Hans-Peter A. Künzi,et al.  Sobrification and bicompletion of totally bounded quasi-uniform spaces , 1987, Mathematical Proceedings of the Cambridge Philosophical Society.

[42]  J. W. Carlson.  Quotient structures for quasi-uniform spaces , 1976 .

[43]  Ralph Kopperman,et al.  Lengths on semigroups and groups , 1982 .

[44]  R. Hodel.  A History of Generalized Metrizable Spaces , 1998 .

[45]  V. Niemytzki.  Über die Axiome des metrischen Raumes , 1931 .

[46]  T. Hicks,et al.  A Note on Locally Quasi-Uniform Spaces , 1976, Canadian Mathematical Bulletin.

[47]  B. Windels.  The Scott Approach Structure: An Extension of the Scott Topology for Quantitative Domain Theory , 2000 .

[48]  R. Lowen,et al.  The cartesian closed hull of the category of approach spaces , 2001 .

[49]  P. Fletcher,et al.  ON BOUNDEDLY METACOMPACT AND BOUNDEDLY PARACOMPACT SPACES , 1970 .

[50]  P. Lambrinos.  Quasi proximal continuity , 1973, Bulletin of the Australian Mathematical Society.

[51]  D. Burke.  Orthocompactness and perfect mappings , 1980 .

[52]  Massood Seyedin.  Quasi-Uniform Spaces and Topological Homeomorphism Groups(1) , 1974, Canadian Mathematical Bulletin.

[53]  G. Richardson.  R 1, Pairwise Compact, and Pairwise Complete Spaces , 1972, Canadian Mathematical Bulletin.

[54]  Basis properties of topologies compatible with (not necessarily symmetric) distance-functions , 1978 .

[55]  P. Fletcher,et al.  The comparison of topologies , 1969 .

[56]  J. D. Lawson,et al.  Order and strongly sober compactifications , 1991 .

[57]  Labib Haddad,et al.  Sur quelques points de topologie générale. Théorie des nasses et des tramails , 1970 .

[58]  Stephen Watson.  The classification of metrics and multivariate statistical analysis 1 This paper was intended as par , 1999 .

[59]  J. Cunningham,et al.  Free trees and bidirectional trees as representations of psychological distance , 1978 .

[60]  Robert Lowen,et al.  A Unified Functional Look at Completion in MET, UNIF and AP , 2000, Appl. Categorical Struct..

[61]  Jacob Kofner.  Open compact mappings, Moore spaces and orthocompactness , 1982 .

[62]  Young-kyoung Kim.  Cauchy Completions of Quasi-uniform Frames , 1998 .

[63]  W. A. Beyer,et al.  Some Biological Sequence Metrics , 1976 .

[64]  S. Romaguera,et al.  Bounded subsets and Grothendieck's theorem for bispaces , 1999 .

[65]  On half-completion and bicompletion of quasi-metric spaces , 1996 .

[66]  J. Blatter.  Order compactifications of totally ordered topological spaces , 1975 .

[67]  P. Fletcher,et al.  On totally bounded quasi-uniform spaces , 1970 .

[68]  I. Reilly,et al.  A new bitopological paracompactness , 1986, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[69]  Ralph Kopperman,et al.  Asymmetry and duality in topology , 1995 .

[70]  H. Render.  Nonstandard methods of completing quasi-uniform spaces , 1995 .

[71]  W. Hunsaker,et al.  Construction of quasi-uniformities , 1970 .

[72]  M. Sion,et al.  Hausdorff measures on abstract spaces , 1966 .

[73]  H. Render.  Hausdorff completions of quasi-uniform spaces , 1996 .

[74]  The Number of Compatible Totally Bounded Quasi-Uniformities , 2000 .

[75]  Jacob Kofner.  Transitivity and Ortho-Bases , 1981, Canadian Journal of Mathematics.

[76]  J. W. Carlson,et al.  On completeness in quasi-uniform spaces , 1971 .

[77]  L. M. Brown.  On topological spaces with a unique compatible quasi-uniformity , 1977, Glasgow Mathematical Journal.

[78]  Ralph Kopperman,et al.  Which topologies are quasimetrizable , 1993 .

[79]  E. Steiner.  The relation between quasi-proximities and topological spaces , 1964 .

[80]  William J. Pervin,et al.  Quasi-uniformization of topological spaces , 1962 .

[81]  M. Mansfield.  Some generalizations of full normality , 1957 .

[82]  R. Kopperman,et al.  Oxtoby's pseudocompleteness revisited , 2000 .

[83]  A note on sequentially compact quasi-pseudo-metric spaces , 1983 .

[84]  Decomposition Properties of Hyperspace Topologies , 1997 .

[85]  H. Junnila.  Covering properties and quasi-uniformities of topological spaces. , 1978 .

[86]  D. Kent,et al.  Ordered probabilistic metric spaces , 1989 .

[87]  J. W. Carlson,et al.  Some properties of quasi-uniform structures , 1973 .

[88]  P. Fletcher.  On completeness of quasi-uniform spaces , 1971 .

[89]  Doitchin Doitchinov,et al.  A concept of completeness of quasi-uniform spaces , 1991 .

[90]  Phan Quoc Khanh.  On general open mapping theorems , 1989 .

[91]  Doitchin Doitchinov,et al.  On completeness in quasi-metric spaces , 1988 .

[92]  P. Fletcher.  Note on quasi-uniform spaces and representable spaces , 1971 .

[93]  Frans Gool,et al.  Lower semicontinuous functions with values in a continuous lattice , 1992 .

[94]  R. Kopperman,et al.  Joincompact spaces, continuous lattices, and C*-algebras , 1997 .

[95]  Bob Flagg.  Algebraic theories of compact pospaces , 1997 .

[96]  Ronald A. Stoltenberg.  A COMPLETION FOR A QUASI UNIFORM SPACE , 1967 .

[97]  R. Hansell,et al.  Borel measurable mappings for nonseparable metric spaces , 1971 .

[98]  F. Hausdorff.  Grundzüge der Mengenlehre , 1914 .

[99]  Michael B. Smyth,et al.  Quasi Uniformities: Reconciling Domains with Metric Spaces , 1987, MFPS.

[100]  J. Aarts,et al.  Complete Regularity as a Separation Axiom , 1969, Canadian Journal of Mathematics.

[101]  H. Anton,et al.  Separation axioms and metric-like functions. , 1976 .

[102]  M. Nauwelaerts.  Some Cartesian Closed Topological Constructs in the Category of Semi-Approach Uniform Limit Spaces , 2000 .

[103]  Philipp Sünderhauf,et al.  Quasi-uniform completeness in terms of Cauchy nets , 1995 .

[104]  A. Frink.  Distance functions and the metrization problem , 1937 .

[105]  R. Fox,et al.  A regular counterexample to the -space conjecture , 1985 .

[106]  P. Fletcher,et al.  Topologies compatible with homeomorphism groups. , 1975 .

[107]  Hans-Peter A. Künzi,et al.  On strongly quasi-metrizable spaces , 1983 .

[108]  Krzysztof Ciesielski,et al.  Polish spaces, computable approximations, and bitopological spaces , 2002 .

[109]  Michael A. Bukatin,et al.  Towards Computing Distances Between Programs via Scott Domains , 1997, LFCS.

[110]  Semilattices of Ordered Compactifications , 1997 .

[111]  H. Künzi,et al.  Quasi-metric spaces, quasi-metric hyperspaces and uniform local compactness , 1999 .

[112]  S. McCartan,et al.  Separation axioms for topological ordered spaces , 1968, Mathematical Proceedings of the Cambridge Philosophical Society.

[113]  Philipp Sünderhauf.  Spaces of valuations as quasimetric domains , 1998, Electron. Notes Theor. Comput. Sci..

[114]  Jorge Picado,et al.  Frames with Transitive Structures , 2002, Appl. Categorical Struct..

[115]  Horst Herrlich,et al.  The Historical Development of Uniform, Proximal, and Nearness Concepts in Topology , 1998 .

[116]  H. Junnila,et al.  Closure-preserving covers by small sets , 1986 .

[117]  Hans-Peter A. KtiNZI.  Completely Regular Ordered Spaces , 1990 .

[118]  H. Künzi,et al.  Some remarks on Doitchinov completeness , 1996 .

[119]  V. Gregori,et al.  On a class of real normed lattices , 1998 .

[120]  S. Romaguera,et al.  On the Bitopological Extension of the Bing Metrization Theorem , 1988, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[121]  J. Blatter,et al.  Interposition and lattice cones of functions , 1976 .

[122]  Ralph Kopperman,et al.  All topologies come from generalized metrics , 1988 .

[123]  Yukinobu Yajima.  A characterization of submetacompactness in terms of products , 1991 .

[124]  Michel P. Schellekens,et al.  The Smyth completion: a common foundation for denotational semantics and complexity analysis , 1995, MFPS.

[125]  A. Davis,et al.  Indexed Systems of Neighborhoods for General Topological Spaces , 1961 .

[126]  H. Kunzi.  Complete quasi-pseudo-metric spaces , 1992 .

[127]  M. J. Pérez-Peñalver,et al.  Weakly Cauchy Filters and Quasi-Uniform Completeness , 1999 .

[128]  M. Nauwelaerts.  The Cartesian Closed Topological Hull of the Category of (Quasi-)Uniform Spaces (Revisited) , 2001 .

[129]  G. Herden.  On a lifting theorem of Nachbin , 1990 .

[130]  A. W. Roscoe,et al.  Topology and category theory in computer science , 1991 .

[131]  DIEUDONN ÉCOMPLETE BISPACES , 2000 .

[132]  P. Gartside,et al.  A note on proto-metrisable spaces , 1993 .

[133]  P. Fletcher,et al.  On almost complete and almost precompact quasi-uniform spaces , 1971 .

[134]  R. Pol.  A perfectly normal locally metrizable non-paracompact space , 1977 .

[135]  I. Reilly.  A generalized contraction principle , 1974, Bulletin of the Australian Mathematical Society.

[136]  S. J. O''Neill,et al.  Partial Metrics, Valuations, and Domain Theory , 1995 .

[137]  P. Fletcher,et al.  Locally quasi-uniform spaces with countable bases , 1974 .

[138]  Ralph Kopperman,et al.  Tychonoff Poset Structures and Auxiliary Relations , 1995 .

[139]  Fletcher.  Quasi-Uniform Spaces , 1982 .

[140]  Andrei Dmitruk,et al.  LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA , 1980 .

[141]  Marcel Erné.  Ideal Completions and Compactifications , 2001, Appl. Categorical Struct..

[142]  Salvador Romaguera,et al.  The quasi-metric of complexity convergence , 2000 .

[143]  Marcello M. Bonsangue,et al.  Generalized Metric Spaces: Completion, Topology, and Powerdomains via the Yoneda Embedding , 1995, Theor. Comput. Sci..

[144]  Ljubomir Ćirić.  Periodic and fixed point theorems in a quasi-metric space , 1993 .

[145]  W. Lindgren.  Topological spaces with unique quasi-uniform structure , 1971 .

[146]  The fuzzy Hausdorff-Bourbaki structures and their relations with the fuzzy Vietoris structures , 1989 .

[147]  S. G. Matthews,et al.  Partial Metric Topology , 1994 .

[148]  L. Skula.  On a reflective subcategory of the category of all topological spaces. , 1969 .

[149]  S. Romaguera.  On hereditary precompactness and completeness in quasi-uniform spaces , 1996 .

[150]  P. V. Subrahmanyam,et al.  Some fixed point theorems , 1992, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[151]  P. Fletcher,et al.  Quasi-uniformities with a transitive base. , 1972 .

[152]  Abbas Edalat,et al.  A Computational Model for Metric Spaces , 1998, Theor. Comput. Sci..

[153]  P. Fletcher,et al.  Transitive quasi-uniformities , 1972 .

[154]  H. Simmons,et al.  A couple of triples , 1982 .

[155]  H. Bennett.  QUASI-METRIZABILITY AND THE ∞-SPACE PROPERTY IN CERTAIN GENERALIZED ORDERED SPACES , 1979 .

[156]  W. Lindgren,et al.  Spaces with bases satisfying certain order and intersection properties , 1976 .

[157]  R. Heath.  A CONSTRUCTION OF A QUASI-METRIC SOUSLIN SPACE WITH A POINT-COUNTABLE BASE , 1977 .

[158]  H. Künzi,et al.  Separation and Epimorphisms in Quasi-Uniform Spaces , 2000 .

[159]  The existence of compatible nontransitive totally bounded quasi-uniformities ✩ , 2002 .

[160]  G. Brümmer.  ON CERTAIN FACTORIZATIONS OF FUNCTORS INTO THE CATEGORY OF QUASI-UNIFORM SPACES , 1977 .

[161]  Alexander P. Sostak,et al.  FUZZY SYNTOPOGENEOUS STRUCTURES , 1997 .

[162]  Wataru Takahashi,et al.  NONCONVEX MINIMIZATION THEOREMS AND FIXED POINT THEOREMS IN COMPLETE METRIC SPACES , 1996 .

[163]  H. Künzi.  A note on uniform ordered spaces , 1987, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[164]  H. Künzi,et al.  Quasi-uniformities on topological semigroups and bicompletion , 2001 .

[165]  Completeness using pairs of filters , 1992 .

[166]  H. Künzi,et al.  Extension properties induced by complete quasi-uniformities , 1985 .

[167]  R. Fox.  Shorter Notes: A Short Proof of the Junnila Quasi-Metrization Theorem , 1981 .

[168]  I. Reilly,et al.  Uniformization of quasi-uniform spaces , 1981, Bulletin of the Australian Mathematical Society.

[169]  S. Levi,et al.  Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions , 1985 .

[170]  Brian M. Scott.  MORE ABOUT ORTHOCOMPACTNESS , 1980 .

[171]  M. J. Canfell.  Semi-algebras and rings of continuous functions , 1969 .

[172]  E. Lowen,et al.  Topological quasitopos hulls of categories containing topological and metric objects , 1989 .

[173]  R. Heath.  Some nonmetric, first countable, cancellative topological semigroups that are generalized metric spaces , 1992 .

[174]  B. Hutton,et al.  Uniformities on fuzzy topological spaces , 1977 .

[175]  I. Reilly,et al.  Metrizability of Quasi‐Metric Spaces , 1977 .

[176]  Hans-Peter A. Künzi,et al.  Ortho-bases and monotonic properties , 1993 .

[177]  T. Mackowiak.  On decompositions of hereditarily smooth continua , 1977 .

[178]  Bernhard Banaschewski,et al.  STRONG ZERO-DIMENSIONALITY OF BIFRAMES AND BISPACES , 1990 .

[179]  Robert Lowen,et al.  A Unif, a common supercategory of pMET and Unif , 1998 .

[180]  Michael A. Bukatin,et al.  Partial Metrics and Co-continuous Valuations , 1998, FoSSaCS.

[181]  J. Aarts,et al.  Pairwise complete regularity as a separation axiom , 1990, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[182]  R. Lowen,et al.  A Wallman-Shanin-Type Compactification for Approach Spaces , 2000 .

[183]  S. Naimpally.  Function Spaces of Quasi-uniform Spaces , 1965 .

[184]  J. Picado.  Weil uniformities for frames , 1995 .

[185]  H. Künzi,et al.  A quasi-metric space without complete quasi-uniformity , 1996 .

[186]  R. F. Gittings.  Finite-to-one open maps of generalized metric spaces. , 1975 .

[187]  Peter Fletcher,et al.  A Construction of the Pair Completion of a Quasi-Uniform Space , 1978, Canadian Mathematical Bulletin.

[188]  S. Salbany.  Quasi-Metrization of bitopological spaces , 1972 .

[189]  K. Porter.  THE REGULAR OPEN-OPEN TOPOLOGY FOR FUNCTION SPACES , 1996 .

[190]  Valentín Gregori,et al.  Fixed point theorems for fuzzy mappings in quasi-metric spaces , 2000, Fuzzy Sets Syst..

[191]  P. Samuel,et al.  Ultrafilters and compactification of uniform spaces , 1948 .

[192]  D. Gauld.  On c-continuous fundamental groups , 1977 .

[193]  Ralph Fox.  A short proof of the Junnila quasimetrization theorem , 1981 .

[194]  Michel P. Schellekens,et al.  Norm-weightable Riesz spaces and the dual complexity space , 2002, Electron. Notes Theor. Comput. Sci..

[195]  M. B. Smyth.  Completeness of Quasi‐Uniform and Syntopological Spaces , 1994 .

[196]  R. Lowen,et al.  Compactifications of products of metric spaces and their relations to Čech-Stone and Smirnov compactifications , 1994 .

[197]  L. E. Ward.  Partially ordered topological spaces , 1954 .

[198]  W. Lindgren.  Topological Spaces with a Unique Compatible Quasi-Uniformity , 1971, Canadian Mathematical Bulletin.

[199]  Wang Guo-jun,et al.  Theory of topological molecular lattices , 1992 .

[200]  Giuseppe Di Maio,et al.  Recent progress in function spaces , 1998 .

[201]  R. Lowen.  Approach Spaces A Common Supercategory of TOP and MET , 1989 .

[202]  Some properties of quasiuniform multifunction spaces , 1998 .

[203]  E. Lowen,et al.  A QUASITOPOS CONTAINING CONV AND MET AS FULL SUBCATEGORIES , 1988 .

[204]  Mark Sioen,et al.  On the Epireflectivity of the Wallman–Shanin-Type Compactification for Approach Spaces , 2000, Appl. Categorical Struct..

[205]  P. Fletcher,et al.  C-complete quasi-uniform spaces , 1978 .

[206]  Salvador Romaguera Bonilla,et al.  Quasi-metrizable spaces with a bicomplete structure. , 1992 .

[207]  H. L. Bentley,et al.  Cauchy Sequences in Quasi-Uniform Spaces: Categorical Aspects , 1988, Categorial Methods in Computer Science.

[208]  Hans-Peter A. Künzi,et al.  Weighted Quasi‐Metrics , 1994 .

[209]  R. Lowen,et al.  On the quantification of uniform properties , 1997 .

[210]  Kamal El-Saady,et al.  Fuzzy proximity ordered spaces , 1999, Fuzzy Sets Syst..

[211]  P. Fletcher,et al.  A Theory of Uniformities for Generalized Ordered Spaces , 1979, Canadian Journal of Mathematics.

[212]  J. W. Carlson.  Nearness and quasi-uniform structures , 1983 .

[213]  T. Hicks,et al.  Some Results on Quasi-Uniform Spaces , 1976, Canadian Mathematical Bulletin.

[214]  Kenneth Kunen,et al.  Handbook of Set-Theoretic Topology , 1988 .

[215]  P. Ribenboim,et al.  Generalized ultrametric spaces II , 1996 .

[216]  Gilles Berthiaume,et al.  On quasi-uniformities in hyperspaces , 1977 .

[217]  Todor D. Todorov,et al.  Nonstandard and standard compactifications of ordered topological spaces , 1992 .

[218]  H. Künzi.  Topological Spaces with a Unique Compatible Quasi-Uniformity , 1986, Canadian Mathematical Bulletin.

[219]  R. Lowen,et al.  Measures of Lindelöf and separability in approach spaces. , 1994 .

[220]  Ralph Kopperman,et al.  Fixed points and reflexive domain equations in categories of continuity spaces , 1995, MFPS.

[221]  Peter Fletcher,et al.  Some unsolved problems concerning countably compact spaces , 1975 .

[222]  J. Aarts,et al.  A bitopological view on cocompact extensions , 1991 .

[223]  B. Banaschewski,et al.  BIFRAMES AND BISPACES , 1983 .

[224]  Salvador Romaguera,et al.  Quasi-metric properties of complexity spaces , 1999 .

[225]  Salvador Romaguera,et al.  Left K‐Completeness in Quasi‐Metric Spaces , 1992 .

[226]  W. Marciszewski,et al.  Absolute Borel sets and function spaces , 1997 .

[227]  Michel Schellekens.  On Upper Weightable Spaces , 1996 .

[228]  Paul Brock,et al.  On Convergence Approach Spaces , 1998, Appl. Categorical Struct..

[229]  Salvador Romaguera,et al.  Well-quasi-ordering and the Hausdorff quasi-uniformity☆ , 1998 .

[230]  R. Flagg,et al.  Quantales and continuity spaces , 1997 .

[231]  H. Künzi,et al.  A topological space without a complete quasi-uniformity , 1984 .

[232]  H. Junnila,et al.  Characterizations of absolute Fσδ-sets , 1998 .

[233]  H. Künzi.  Kelley's conjecture and preorthocompactness , 1987 .

[234]  Robert Lowen.  KURATOWSKI'S MEASURE OF NON-COMPACTNESS REVISITED , 1988 .

[235]  Coverings versus entourages , 1998 .

[236]  J. Ferrer,et al.  A Note on R. Stoltenberg's Completion Theory of Quasi-Uniform Spaces , 1984 .

[237]  TOPOLOGICAL SPACES WITH A COARSEST COMPATIBLE QUASI-PROXIMITY , 1986 .

[238]  Hans-Peter A. Künzi,et al.  Completely regular ordered spaces , 1990 .

[239]  Jacob Kofner.  Closed mappings and quasimetrics , 1980 .

[240]  M. B. Smyth,et al.  Stable compactification I , 1992 .

[241]  S. Romaguera.  On Complete Aronszajn Quasi‐metric Spaces and Subcompactness , 1994 .

[242]  P. Fletcher.  Homeomorphism groups with the topology of quasi-uniform convergence , 1971 .

[243]  R. Lowen,et al.  The Wijsman and Attouch-Wets topologies on hyperspaces revisited , 1996 .

[244]  A. Andrikopoulos,et al.  The coregular property on γ-spaces , 1999 .

[245]  A. Losonczi.  Special Simultaneous Quasi-uniform Extensions , 1999 .

[246]  M. Sion,et al.  On Quasi-Metrizability , 1967, Canadian Journal of Mathematics.

[247]  Philipp Sünderhauf,et al.  Uniform approximation of topological spaces , 1998 .

[248]  S. Romaguera.  Two characterizations of quasi-pseudometrizable bitopological spaces , 1983, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[249]  G. E. Albert.  A note on quasi-metric spaces , 1941 .

[250]  D. Doitchinov.  ANOTHER CLASS OF COMPLETABLE QUASI-UNIFORM SPACES , 1991 .

[251]  Valentín Gregori,et al.  Quasi-uniform Structures in Linear Lattices , 1993 .

[252]  R. Lowen,et al.  Approach Theory in Merotopic, Cauchy and Convergence Spaces. II , 1999 .

[253]  Michael B. Smyth,et al.  Totally bounded spaces and compact ordered spaces as domains of computation , 1991 .

[254]  S. Romaguera,et al.  Pairwise monotonically normal spaces , 1991 .

[255]  Fuzzy syntopogenous structures and order , 1994 .

[256]  R. Hodel.  Spaces defined by sequences of open covers which guarantee that certain sequences have cluster points , 1972 .

[257]  S. Romaguera,et al.  On Right K-Sequentially Complete Quasi-Metric Spaces , 1997 .

[258]  R. Lowen,et al.  Proximal Hypertopologies Revisited , 1998 .

[259]  Fuzzy quasi uniformities and fuzzy bitopological spaces , 1992 .

[260]  M. Vamanamurthy,et al.  COMPARISON OF CONVERGENCES FOR MULTIFUNCTIONS , 1997 .

[261]  E. Michael.  Topologies on spaces of subsets , 1951 .

[262]  Ivan L. Reilly.  On generating quasi uniformities , 1970 .

[263]  S. Romaguera.  On bitopological quasi-pseudometrization , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[264]  E. Reznichenko.  Extension of functions defined on products of pseudocompact spaces and continuity of the inverse in pseudocompact groups , 1994 .

[265]  Bobby Schmidt,et al.  Fuzzy math , 2001 .

[266]  Reinhold Heckmann,et al.  Approximation of Metric Spaces by Partial Metric Spaces , 1999, Appl. Categorical Struct..

[267]  L. S. Pontryagin,et al.  General Topology I , 1990 .

[268]  Measures of compactness in approach spaces , 1995 .

[269]  Jacob Kofner.  Transitivity and the -space conjecture in ordered spaces , 1981 .

[270]  A sequentially compact non-compact quasi-pseudometric space , 1983 .

[271]  Á. Száz.  Basic tools and mild continuities in relator spaces , 1987 .

[272]  I. Reilly.  Zero dimensional bitopological spaces , 1973 .

[273]  M. Nauwelaerts.  Cartesian closed hull for (quasi-)metric spaces (revisited) , 2000 .

[274]  W. Pervin.  Quasi-proximities for topological spaces , 1963 .

[275]  Ivan L. Reilly,et al.  Quasi-Gauge Spaces , 1973 .

[276]  S. Salbany.  Linearly Ordered Topologies and Quasi‐metrization , 1995 .

[277]  I. Reilly,et al.  Characterizations of Quasi-Metrizable Bitopological Spaces , 1988, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[278]  Paul Brock,et al.  Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces , 1997, Appl. Categorical Struct..

[279]  On convergence complete strong quasi-metrics , 1994 .

[280]  J. J. M. M. Rutten.  Weighted colimits and formal balls in generalized metric spaces , 1997 .

[281]  M.M. BONSANGUE,et al.  Alexandroff and Scott Topologies for Generalized Metric Spaces , 1996 .

[282]  Paolo Vitolo.  A representation theorem for quasi-metric spaces , 1995 .

[283]  M. Ganster,et al.  On pairwise paracompactness , 1992, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[284]  Norman R. Howes,et al.  Modern Analysis and Topology , 1995 .

[285]  Hans-Peter A. Künzi,et al.  Borel classification via quasi-metrics , 1997 .

[286]  Rudolf-E. Hoffmann,et al.  On the sobrification remainder $^{s}X-X$. , 1979 .

[287]  L. Nachbin.  Topology and order , 1965 .

[288]  W. A. Wilson.  On Quasi-Metric Spaces , 1931 .

[289]  R. Z. Domiaty.  Life without T2 , 1981 .

[290]  F. William Lawvere,et al.  Metric spaces, generalized logic, and closed categories , 1973 .

[291]  H. Künzi.  Strongly zero-dimensional bispaces , 1992, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[292]  Peter Fletcher,et al.  Entourage uniformities for frames , 1991 .

[293]  K. Porter.  Some Equivalent Topologies on Homeomorphism Groups , 1997 .

[294]  J. Golan.  More topologies on the torsion-theoretic spectrum of a ring , 1990 .

[295]  Quasi-uniform hyperspaces of compact subsets , 1998 .

[296]  Salvador Romaguera,et al.  Semi-Lipschitz Functions and Best Approximation in Quasi-Metric Spaces , 2000 .

[297]  R. Stoltenberg,et al.  Some Properties of Quasi‐Uniform Spaces , 1967 .

[298]  R. Lowen.  Cantor-connectedness revisited , 1992 .

[299]  R. Stoltenberg.  On quasi-metric spaces , 1969 .

[300]  H. Künzi.  Quasi Uniformities Defined by Sets of Neighborhoods a , 1992 .

[301]  Hilary A. Priestley,et al.  Ordered Topological Spaces and the Representation of Distributive Lattices , 1972 .

[302]  A topological category suited for approximation theory , 1989 .

[303]  J. M. G. Fell,et al.  A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space , 1962 .

[304]  R. Lowen,et al.  Local compactness in approach spaces II , 1998 .

[305]  H. Künzi.  Topological spaces with a unique compatible quasi-proximity , 1984 .

[306]  Hans Weber.  Uniform lattices , 1991 .