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Topological groups close to being σ-compact

✍ Scribed by Constancio Hernández

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
110 KB
Volume
102
Category
Article
ISSN
0166-8641

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✦ Synopsis

Two new classes of topological groups are introduced: o-bounded and strictly o-bounded groups. We give an example of a topological group which is strictly o-bounded but is not a subgroup of a σ -compact group. A characterization of o-bounded groups in terms of their second countable continuous homomorphic images is presented. Also, we construct a topological group which is o-bounded but not strictly o-bounded.

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## Abstract Let __G__ be a compact Hausdorff group. A subspace __X__ of __G topologically generates G__ if __G__ is the smallest closed subgroup of __G__ containing __X__. Define __tgw__ (__G__) = __ω__ · min{__w__ (__X__): __X__ is closed in __G__ and topologically generates __G__ }, where __w__