On ν-embedded sets in topological spaces

Blair, Robert L.

doi:10.1007/bfb0068459

Cited by 10 publications

(9 citation statements)

References 15 publications

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“…We start with extensions to frames of two theorems of Blair's [8,Lemma 3.9] and [7,Lemma 6.3]. The first states that if a Tychonoff space is a countable union of realcompact z-embedded subspaces, then it is realcompact.…”

Section: Miscellaneous Resultsmentioning

confidence: 99%

Realcompactness and certain types of subframes

Dube

2008

Algebra univers.

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If a frame satisfies a property which is some variant of realcompactness, then certain types of its subframes inherit the property. Conversely, there are instances where a frame has a subframe satisfying some such property only if the frame itself satisfies the property. We analyze these phenomena for the case of realcompactness, almost realcompactness, a-realcompactness, c-realcompactness and weak realcompactness vis-a-vis perfect subframes and flat subframes.

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Section: Miscellaneous Resultsmentioning

confidence: 99%

Realcompactness and certain types of subframes

Dube

2008

Algebra univers.

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“…This corollary follows from 1.2(2) and 1.4 (2). Note here that for any zeroset Z the concepts of C-, C*-, and z-embedding are all equivalent [1, 7.5].…”

Section: Corollary 15 £/ ^4 and A Realcompact Closed Subset Of X Suchmentioning

confidence: 90%

Union of Realcompact Spaces and Lindelöf Spaces

Kato¹

1979

Can. j. math.

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All spaces in this paper are completely regular Hausdorff and all maps are continuous onto, unless otherwise stated. The purpose of this paper is to investigate the realcompactness of a space X which contains a Lindelöf space L such that every zero-set Z (in X) disjoint from L is realcompact. We show in § 2 that such a space X is very close to being realcompact (Theorems I, II and III). But in general such a space fails to be realcompact. Indeed, in §§ 3 and 4 the following questions of Mrówka [18, 19] are answered, both in the negative:(Q. 1) If X = L ∪ G where L is Lindelöf closed and G is E-compact, then is X E-compact?(Q. 2) Suppose f:X → Y is a perfect map such that the set M(f) = {y ∊ Y| |f−l(y)| > 1} of multiple points of f is Lindelöf (especially, countable) closed. If X is E-compact, is Y also E-compact?

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“…Blair studied u-embedding in [1]. A useful discussion of this type of embedding may be found in [9].…”

Section: A-embeddingmentioning

confidence: 99%

The pseudocompact extension 𝛼𝑋

Aull¹,

Sawyer²

1988

Proc. Amer. Math. Soc.

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ABSTRACT. For any Tychonoff space we define aX = [ßX -vX) U X = ßX -(vX -X). We show that aX is the smallest pseudocompactification Y of X contained is ßX such that every free hyperreal z-ultrafilter on X converges in Y and is the largest pseudocompactification V of X contained in ßX such that every point in Y -X is contained in a zero set of Y which does not intersect X. A space S is defined to be a-embedded in a space X if aS C ßX. Properties of a-embeddings and its relation to u-embeddings of Blair C*-embeddings, C-embeddings, and well-embeddings are investigated. For instance, if S is a-embedded and dense in X, S is fully well-embedded (for P, R C X, where ScPCfiCX, Pis well-embedded in R) in X iff aX-aS = X -S.

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On ν-embedded sets in topological spaces

Cited by 10 publications

References 15 publications

Realcompactness and certain types of subframes

Realcompactness and certain types of subframes

Union of Realcompact Spaces and Lindelöf Spaces

The pseudocompact extension 𝛼𝑋

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