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Free topological groups over metrizable spaces

✍ Scribed by A.V. Arhangel'skiǐ; O.G. Okunev; V.G. Pestov


Book ID
107913734
Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
828 KB
Volume
33
Category
Article
ISSN
0166-8641

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📜 SIMILAR VOLUMES


Free topological groups on metrizable sp
✍ Vladimir Pestov; Kohzo Yamada 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 107 KB

We prove that for a metrizable space X the following are equivalent: (i) the free Abelian topological group A(X) is the inductive limit of the sequence {A n (X): n ∈ N}, where A n (X) is formed by all words of reduced length n; (ii) X is locally compact and the set of all non-isolated points of X is

Free topological groups of weak P-spaces
✍ Warren Wm. McGovern 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 55 KB

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