Categorical properties of L-fuzzifying convergence spaces

In this paper, categorical properties of L-fuzzifying convergence spaces are investigated. It is shown that (1) the category L-FYC of L-fuzzifying convergence spaces is a strong topological universe; (2) the category L-FYKC of L-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective subcategory of L-FYC, is also a strong topological universe; (3) the category L-FYLC of L-fuzzifying limit spaces, as a bireflective subcategory of L-FYKC, is a topological universe.

[1]  Alexander P. Sostak,et al.  Axiomatic Foundations Of Fixed-Basis Fuzzy Topology , 1999 .

[2]  Jinming Fang,et al.  Relationships between L-ordered convergence structures and strong L-topologies , 2010, Fuzzy Sets Syst..

[3]  Kai Hu,et al.  The lower and upper p-topological (p-regular) modifications for lattice-valued convergence spaces , 2016, Fuzzy Sets Syst..

[4]  Bin Pang.  The category of stratified L-filter spaces , 2014, Fuzzy Sets Syst..

[5]  Jinming Fang,et al.  Lattice-valued semiuniform convergence spaces , 2012, Fuzzy Sets Syst..

[6]  Zhen-Yu Xiu,et al.  BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES , 2017 .

[7]  Bin Pang,et al.  Stratified L-ordered filter spaces , 2017 .

[8]  Giles Richardson,et al.  Lattice-valued spaces: Fuzzy convergence , 2006, Fuzzy Sets Syst..

[9]  Gunther Jäger,et al.  Pretopological and topological lattice-valued convergence spaces , 2007, Fuzzy Sets Syst..

[10]  Gunther Jäger,et al.  Subcategories of lattice-valued convergence spaces , 2005, Fuzzy Sets Syst..

[11]  Sheng-Gang Li,et al.  Completion of stratified (L, M)-filter tower spaces , 2013, Fuzzy Sets Syst..

[12]  Bin Pang,et al.  Stratified L-prefilter convergence structures in stratified L-topological spaces , 2018, Soft Comput..

[13]  Fu-Gui Shi,et al.  Degrees of compactness in (L, M)-fuzzy convergence spaces and its applications , 2014, Fuzzy Sets Syst..

[14]  Fu-Gui Shi,et al.  Subcategories of the category of L-convex spaces , 2017, Fuzzy Sets Syst..

[15]  Bin Pang,et al.  L-fuzzy Q-convergence structures , 2011, Fuzzy Sets Syst..

[16]  Wei Yao.  ON L-FUZZIFYING CONVERGENCE SPACES , 2009 .

[17]  Jinming Fang,et al.  Stratified L-ordered quasiuniform limit spaces , 2013, Fuzzy Sets Syst..

[18]  Fang Jinming,et al.  Stratified L-ordered convergence structures , 2010, Fuzzy Sets Syst..

[19]  Gerhard Preuss,et al.  Foundations of Topology: An Approach to Convenient Topology , 2002 .

[20]  Qiu Jin,et al.  On stratified L-convergence spaces: Pretopological axioms and diagonal axioms , 2012, Fuzzy Sets Syst..

[21]  Gunther Jäger,et al.  Connectedness and local connectedness for lattice-valued convergence spaces , 2016, Fuzzy Sets Syst..

[22]  Bin Pang,et al.  M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces , 2017, J. Intell. Fuzzy Syst..

[23]  Gunther Jäger,et al.  A CATEGORY OF L-FUZZY CONVERGENCE SPACES , 2001 .

[24]  Kai Hu,et al.  On stratified L-convergence spaces: Fischer's diagonal axiom , 2015, Fuzzy Sets Syst..

[25]  Fu-Gui Shi,et al.  Characterizations of L-convex spaces via domain theory , 2020, Fuzzy Sets Syst..

[26]  Qiu Jin,et al.  On adjunctions between Lim, SL-Top, and SL-Lim , 2011, Fuzzy Sets Syst..

[27]  Bin Pang,et al.  Degrees of separation properties in stratified L-generalized convergence spaces using residual implication , 2017 .

[28]  Bin Pang,et al.  CHARACTERIZATIONS OF L-CONVEX SPACES , 2016 .

[29]  U. Höhle,et al.  Characterization Of L-Topologies By L-Valued Neighborhoods , 1999 .

[30]  Bin Pang.  On (L, M)-fuzzy convergence spaces , 2014, Fuzzy Sets Syst..

[31]  Zhen-Yu Xiu,et al.  Lattice-Valued Interval Operators and Its Induced Lattice-Valued Convex Structures , 2018, IEEE Transactions on Fuzzy Systems.

[32]  Gunther Jäger.  Stratified LMN-convergence tower spaces , 2016, Fuzzy Sets Syst..

[33]  Fu-Gui Shi,et al.  Strong inclusion orders between L-subsets and its applications in L-convex spaces , 2018 .

[34]  R. Lowen.  Convergence in fuzzy topological spaces , 1977 .

[35]  Wei Yao,et al.  On many-valued stratified L-fuzzy convergence spaces , 2008, Fuzzy Sets Syst..

[36]  Kyung Chan Min,et al.  Fuzzy limit spaces , 1989 .

[37]  Dogan Çoker,et al.  Convergence in I-fuzzy topological spaces , 2005, Fuzzy Sets Syst..

[38]  Jinming Fang,et al.  Lattice-valued preuniform convergence spaces , 2014, Fuzzy Sets Syst..

[39]  Luoshan Xu,et al.  Characterizations of fuzzifying topologies by some limit structures , 2001, Fuzzy Sets Syst..

[40]  Qiu Jin,et al.  p-Topologicalness and p-regularity for lattice-valued convergence spaces , 2014, Fuzzy Sets Syst..

[41]  Bin Pang.  Enriched (L, M)-fuzzy convergence spaces , 2014, J. Intell. Fuzzy Syst..

[42]  Bin Pang.  Further study on $L$-fuzzy Q-convergence structures , 2013 .