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Limits in function spaces and compact groups

โœ Scribed by Joan E. Hart; Kenneth Kunen


Book ID
108286206
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
143 KB
Volume
151
Category
Article
ISSN
0166-8641

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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