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Subjects
54-XX General topology
54Dxx Fairly general properties
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

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Displaying 21 – 24 of 24

Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

Fundamenta Mathematicae

We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a $G_{δ}$ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

Covering properties in countable products, II

Sachio Higuchi, Hidenori Tanaka (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and ${X_{n} : n \in ω}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y \times \prod_{n \in ω} X_{n}$ is subparacompact and (2) If ${X_{n} : n \in ω}$ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod_{n \in ω} X_{n}$ is metacompact.

Criterion of Normality of the Completely Regular Topology of Separate Continuity

Grinshpon, Yakov S. (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous if and only if f : X ~⊗ Y→ Z is continuous. We prove a necessary condition of normality, a sufficient condition of collectionwise normality, and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.

C-scattered and paracompact spaces

Rastislav Telgársky (1971)

Fundamenta Mathematicae

Currently displaying 21 – 24 of 24

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