Resumen de Proper actions on topological groups: Applications to quotient spaces

Sergey A. Antonyan

• 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.