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Realcompactification of frames

Nizar Marcus (1995)

Commentationes Mathematicae Universitatis Carolinae

We give a construction of Wallman-type realcompactifications of a frame L by considering regular sub σ -frames the join of which generates L . In particular, we show that the largest such regular sub σ -frame gives rise to the universal realcompactification of L .

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] and of the...

Relatively realcompact sets and nearly pseudocompact spaces

John J. Schommer (1993)

Commentationes Mathematicae Universitatis Carolinae

A space is said to be nearly pseudocompact iff v X - X is dense in β X - X . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.

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