Free Banach spaces and representations of topological groups
โ Scribed by V. G. Pestov
- Publisher
- Springer US
- Year
- 1986
- Tongue
- English
- Weight
- 259 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0016-2663
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We prove that if X is a Tychonoff topological space, Y a subspace of X, and every bounded continuous pseudometric on Y can be extended to a continuous pseudometric on X, then the free topological group F M (Y ) coincides with the topological subgroup of F M (X) generated by Y . For this purpose, a n
It is known that the free topological group over the Tychonoff space X, denoted F (X), is a Pspace if and only if X is a P -space. This article is concerned with the question of whether one can characterize when F (X) is a weak P -space, that is, a space where all countable subsets are closed. Our m
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D โ D is a normal totality on a Scott domain D if it is upward closed and x y โ D is an equivalence relation on D . We prove that every topological space can be represented by a domain with normal totality.