Countability and semi-uniformities
โ Scribed by A.K. Steiner; E.F. Steiner
- Book ID
- 103096034
- Publisher
- Elsevier Science
- Year
- 1973
- Weight
- 446 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0016-660X
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โฆ Synopsis
It is shown that if a semi-uniformity has a base consisting of countable coversI, xists a compatible finer uniformity.
๐ SIMILAR VOLUMES
This paper is devoted to the problem of selections. An important result in this area is Michael's theorem on double selection for lower semi-continuous closed valued multifunctions. Recently we obtained a generalization of this theorem to a subclass of the so-called generalized metric spaces, namely
A base B for a topological space X is said to be sharp if for every x โ X and every sequence (U n ) nโฯ of pairwise distinct elements of B with x โ U n for all n the set { i<n U i : n โ ฯ} forms a base at x. Sharp bases of T 0 -spaces are weakly uniform. We investigate which spaces with sharp bases