Closures of weakened analytic groups

Author:
T. Christine Stevens

Journal:
Proc. Amer. Math. Soc. **119** (1993), 291-297

MSC:
Primary 22A05; Secondary 22E15

DOI:
https://doi.org/10.1090/S0002-9939-1993-1123667-8

MathSciNet review:
1123667

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Abstract: Let be a topological group with dense subgroup , and suppose that is an analytic group in a topology that is stronger than the topology that inherits from . It is known that contains a -closed abelian subgroup that completely determines the topology of . We now prove that the -closure of similarly determines the topology of . always has a left-completion in the category of topological groups, and the properties of determine whether is locally compact, analytic, metrizable, left-complete, or finite dimensional. We discuss the relationship between these results and recent work of Goto.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1123667-8

Keywords:
Analytic group,
weakened analytic group,
completion of a group

Article copyright:
© Copyright 1993
American Mathematical Society