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Proper actions and proper invariant metrics
Author(s) -
Abels H.,
Manoussos A.,
Noskov G.
Publication year - 2011
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdq091
Subject(s) - mathematics
We show that if a locally compact group G acts properly on a locally compact σ‐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 .