Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/550

 Title: Regular and Other Kinds of Extensions of Topological Spaces Authors: Dimov, G. Keywords: RegularRegular ClosedCompactLocally CompactCompletely RegularCE-RegularExtensionsSR– (R–, RC–, EF–) ProximitiesNearness SpacesOCE– (CE–) Regular Spaces Issue Date: 1998 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 24, No 1, (1998), 99p-126p Abstract: 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] and of the Harris Theorem on regular-closed extensions [17, Thm. H] are given. It is shown that the notion of SR-proximity is a generalization of the notions of RC-proximity [17] and Efremovicˇ proximity [15]. Moreover, there is a natural way for coming to both these notions starting from the SR-proximities. A characterization (in the spirit of M. Lodato [23, 24]) of the proximity relations induced by the regular extensions is given. It is proved that the injectively ordered set of all (up to equivalence) regular extensions of X in which X is 2-combinatorially embedded has a largest element (κX, κ). A construction of κX is proposed. A new class of regular spaces, called CE-regular spaces, is introduced; the class of all OCE-regular spaces of J. Porter and C. Votaw [29] (and, hence, the class of all regular-closed spaces) is its proper subclass. The CE-regular extensions of the regular spaces are studied. It is shown that SR-proximities can be interpreted as bases (or generators) of the subtopological regular nearness spaces of H. Bentley and H. Herrlich [4]. Description: ∗ 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. URI: http://hdl.handle.net/10525/550 ISSN: 1310-6600 Appears in Collections: Volume 24 Number 1

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