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