Normal families and completely regular spaces

Steiner, E. F.

doi:10.1215/s0012-7094-66-03389-8

Cited by 25 publications

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“…realcompact) space. The following notion due to E. F. Steiner is the basic device in the present setting [13,14]. Definition 2.1.…”

Section: Covers and Extensionsmentioning

confidence: 99%

Minimal Quasi-F Covers of Realcompact Spaces

Jeon¹,

Kim²

2016

The Pure and Applied Mathematics

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Abstract. In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QF K of K is also a Wallman compactification of the inverse image Φ −1 K (X) of the space X under the covering map Φ K : QF K −→ K. Using these, we show that for any space X, βQF X = QF βυX and that a realcompact space X is a projective object in the category Rcomp # of all realcompact spaces and their z # -irreducible maps if and only if X is a quasi-F space.

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“…realcompact) space. The following notion due to E. F. Steiner is the basic device in the present setting [13,14]. Definition 2.1.…”

Section: Covers and Extensionsmentioning

confidence: 99%

Minimal Quasi-F Covers of Realcompact Spaces

Jeon¹,

Kim²

2016

The Pure and Applied Mathematics

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“…Frink [4] showed that a Fi-space is completely regular if and only if it has a separating, normal ring. In [13] the second author introduced the concept of a separating nest generated intersection ring which is stronger than that of a separating normal ring and has the additional property that the trace of a separating nest generated intersection ring on any subspace is also such a ring. (Proof given in [13].)…”

Section: Preliminariesmentioning

confidence: 99%

“…In [13] the second author introduced the concept of a separating nest generated intersection ring which is stronger than that of a separating normal ring and has the additional property that the trace of a separating nest generated intersection ring on any subspace is also such a ring. (Proof given in [13].) We now state and outline the proof of some facts concerning nest generated families which will be needed.…”

Section: Preliminariesmentioning

confidence: 99%

Nest Generated Intersection Rings in Tychonoff Spaces

Steiner¹,

Steiner²

1970

Transactions of the American Mathematical Society

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“…It is hardly surprising that one has been looking for characterizations of complete regularity which naturally fit in between the axiom of regularity and that of normality. See, for example, [3], [4], [17] and [ 18]. It seems that the paper [8] has been unnoticed for a long time [2].…”

Section: Introductionmentioning

confidence: 99%

Pairwise complete regularity as a separation axiom

Aarts

Mršević

1990

J Aust Math Soc A

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Focussing on complete regularity, we discuss the separation properties of bitopological spaces. The unifying concept is that of separation by a pair of bases {9S\,3Si) for the closed sets of a bitopological space ( S ,^,^) . For various separation properties a characterization is presented in terms of separation by a pair of closed bases. This is extended to results concerning pairs of subbases. Here the notion of screening by pairs of subbases plays a central role and the characterization of complete regularity in a natural way fits in between those of regularity and normality. In the key lemma the relation with quasi-proximities is exhibited.

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Normal families and completely regular spaces

Cited by 25 publications

References 0 publications

Minimal Quasi-F Covers of Realcompact Spaces

Minimal Quasi-F Covers of Realcompact Spaces

Nest Generated Intersection Rings in Tychonoff Spaces

Pairwise complete regularity as a separation axiom

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