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
✦ LIBER ✦
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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