Proper actions on topological groups: Applications to quotient spaces
- Autores: Sergey A. Antonyan
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 10, 2010, págs. 3707-3716
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10504-x
- Enlaces
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Resumen
Let be a Hausdorff topological group and a locally compact subgroup of . We show that the natural action of on is proper in the sense of R. Palais. This is applied to prove that there exists a closed set such that and the restriction of the quotient projection to is a perfect map . This is a key result to prove that many topological properties (among them, paracompactness and normality) are transferred from to , and some others are transferred from to . Yet another application leads to the inequality for every paracompact topological group and a locally compact subgroup of having a compact group of connected components.
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