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Inductive limits and tensor products of topological algebras

โœ Scribed by Anastasios Mallios


Publisher
Springer
Year
1967
Tongue
English
Weight
495 KB
Volume
170
Category
Article
ISSN
0025-5831

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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 โˆˆ 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