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Regular and Other Kinds of Extensions of Topological Spaces

Dimov, G. — 1998

Serdica Mathematical Journal

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94. In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31]...

A -compactifications and A -weight of Alexandroff spaces

A. CaterinoG. DimovM. C. Vipera — 2002

Bollettino dell'Unione Matematica Italiana

The paper is devoted to the study of the ordered set A K X , α of all, up to equivalence, A -compactifications of an Alexandroff space X , α . The notion of A -weight (denoted by a w X , α ) of an Alexandroff space X , α is introduced and investigated. Using results in ([7]) and ([5]), lattice properties of A K X , α and A K α w X , α are studied, where A K α w X , α is the set of all, up to equivalence, A -compactifications Y of X , α for which w Y = a w X , α . A characterization of the families of bounded functions generating an A -compactification of X , α is obtained. The notion...

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