Proper actions and proper invariant metrics

Details Proper actions and proper invariant metrics Proper actions and proper invariant metrics

2007-02-12

arxiv.org/abs/math/0702322v2

Mathematics

Metric Geometry

The paper has been completely rewritten and differs essentially from "Constructing invariant Heine-Borel metrics for proper G-

Scientific paper

We show that if a (locally compact) group $G$ acts properly on a locally
compact $\sigma$-compact space $X$ then there is a family of $G$-invariant
proper continuous finite-valued pseudometrics which induces the topology of
$X$. If $X$ is furthermore metrizable then $G$ acts properly on $X$ if and only
if there exists a $G$-invariant proper compatible metric on $X$.

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