Invariant proper metrics on coset spaces

Constructing Invariant Heine-borel Metrics for Proper G-spaces

We show that a group G acts properly and effectively on a locally compact and σ-compact metric space (X, d) if and only if there exists a compatible G-invariant Heine-Borel metric dp on X such that G is homeomorphic to a closed subgroup of the group of isometries Iso(X, dp).

Proper actions and proper invariant metrics

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.

Invariant Metrics on G-spaces

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Projective Invariant Metrics for Einstein Spaces