THE ROUND IDEAL COMPLETION VIA SOBRIFICATION

In this paper we consider an important order completion, the rounded-ideal completion, that has arisen in the modern theory of continuous domains. We show that it can be alternately viewed as a special case of a more general topo­ logical method of completion, namely taking the sobrification of a topological space. A number of important special caSes and examples are in­ cluded.

[1]  Samson Abramsky,et al.  Domain theory , 1995, LICS 1995.

[2]  K. Hofmann,et al.  A Compendium of Continuous Lattices , 1980 .

[3]  P. Martin-Löf.  Notes on constructive mathematics , 1970 .

[4]  Rudolf-E. Hoffmann,et al.  Sobrification of partially ordered sets , 1979 .

[5]  Abbas Edalat.  Domain Theory and Integration , 1995, Theor. Comput. Sci..

[6]  Abbas Edalat,et al.  Power Domains and Iterated Function Systems , 1996, Inf. Comput..

[7]  Tsutomu Kamimura,et al.  Total Objects of Domains , 1984, Theor. Comput. Sci..

[8]  Klaus Weihrauch,et al.  Embedding Metric Spaces Into CPO's , 1981, Theor. Comput. Sci..

[9]  Abbas Edalat,et al.  Dynamical Systems, Measures and Fractals via Domain Theory , 1993, Inf. Comput..

[10]  Dana S. Scott,et al.  Outline of a Mathematical Theory of Computation , 1970 .

[11]  N. Saheb-Djahromi,et al.  CPO'S of Measures for Nondeterminism , 1980, Theor. Comput. Sci..

[12]  Michael B. Smyth,et al.  Effectively given Domains , 1977, Theor. Comput. Sci..

[13]  Jimmie D. Lawson,et al.  Spaces of maximal points , 1997, Mathematical Structures in Computer Science.

[14]  Claire Jones,et al.  Probabilistic non-determinism , 1990 .

[15]  C. Jones,et al.  A probabilistic powerdomain of evaluations , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

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