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Point-countable bases and k-networks

✍ Scribed by L. Foged


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
789 KB
Volume
69
Category
Article
ISSN
0166-8641

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πŸ“œ SIMILAR VOLUMES


Sharp bases and weakly uniform bases ver
✍ A.V. Arhangel'skiı̌; W. Just; E.A. Rezniczenko; P.J. Szeptycki πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 86 KB

A base B for a topological space X is said to be sharp if for every x ∈ X and every sequence (U n ) nβˆˆΟ‰ of pairwise distinct elements of B with x ∈ U n for all n the set { i<n U i : n ∈ Ο‰} forms a base at x. Sharp bases of T 0 -spaces are weakly uniform. We investigate which spaces with sharp bases

Closed maps on spaces with point-countab
✍ Alexander Shibakov πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 134 KB

We prove a version of LaΕ‘nev's theorem for spaces with point-countable bases. Then we study the subspaces of closed images of regular spaces with point-countable bases and show that every such subspace has countable Ο€-character and a point-countable Ο€-base. The latter result is extended to a wider

On spaces with point-countable cs-networ
✍ Shou Lin; Chuan Liu πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 473 KB

In this paper we discuss three questions about the quotient s-images of metric spaces. The main results are: (1) X is a sequential space with a point-countable cs-network if and only if X is a compactcovering, sequence-covering, quotient and s-image of a metric space. (2) Let X and Y be sequential

Spaces with a star-countable k-network,
✍ Chuan Liu; Yoshio Tanaka πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 775 KB

Recall that a collection 79 of subsets of a space is star-countable if each element of 7 ~ meets at most countably many other elements of 79. We characterize the closed image of a locally separable metric space as a Frrchet space with a star-countable k-network, and give a characterization for the p