Open Access
A characterization of a/0-spaces
Reads0
Chats0
TLDR
In this article, it was shown that a Tyspace has a o-closure-preserving base consisting of clopen sets if the space can be embedded in the product of countably many o-discrete stratifiable spaces.Abstract:
The following result is obtained. Theorem. A Tyspace has a o-closure-preserving base consisting of clopen sets iff the space can be embedded in the product of countably many o-discrete stratifiable spaces.read more
Citations
More filters
Journal ArticleDOI
On P-spaces and related concepts
Saak Gabriyelyan,J. Ka̧kol +1 more
TL;DR: The strong Pytkeev property of generalized metric spaces was introduced by Tsaban and Zdomskyy in this article, where they showed that any metric space X is a P -space if and only if X is an ℵ 0 -space and Y is a p -space.
Journal ArticleDOI
Function spaces with a countable cs∗-network at a point☆
TL;DR: For a Tychonoff space X, the space of all real-valued continuous functions on X with the topology of pointwise convergence (the compact-open topology) was shown to have a countable cs∗-network at 0 iff X is countable in this paper.
Journal ArticleDOI
On topological spaces and topological groups with certain local countable networks
Saak Gabriyelyan,J. Ka̧kol +1 more
TL;DR: In this article, it was shown that a Baire topological group G is metrizable if and only if G has the strong Pytkeev property and if G is separable and has a countable cp-network at the unit.
Journal ArticleDOI
Networks for the weak topology of Banach and Fréchet spaces
TL;DR: In this paper, it was shown that a reflexive Frechet lcs E in the weak topology is an ℵ-space if and only if E is separable.
Journal ArticleDOI
On topological properties of Fréchet locally convex spaces with the weak topology
TL;DR: In this article, it was shown that a Baire cosmic group is metrizable if and only if the strong dual of the Baire group is separable, which is the case for all locally convex spaces (lcs) under the weak topology σ (E, E, E ).
References
More filters
Journal ArticleDOI
On stratifiable spaces
TL;DR: In this article, it was shown that the closed continuous image of a stratifiable space is stratifiable and the well-known extension theorem of Dugundji remains valid for stratifiable spaces (see Theorem 4.1, Pacific J. Math., 1 (1951), 353-367).
Journal ArticleDOI
On M-structures
TL;DR: In this paper, the notion of M -structures was introduced and the relation between the class M and that of M 1 -spaces was studied in the context of stratifiable spaces with M-structures.
Journal ArticleDOI
Stratifiable spaces as subspaces and continuous images of ₁-spaces
TL;DR: In this paper, it was shown that every stratifiable space is the image of an MI-space under a perfect retraction, and the converse results also hold for non-Tl-spaces.