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 and inductive limits
✍ Scribed by Michael G. Tkačenko
- Book ID
- 107913870
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 882 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0166-8641
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