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arXiv math/0702322math.MGmath.GN
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真作用和真不变度量

Proper actions and proper invariant metrics

Herbert Abels, Antonios Manoussos, Gennady Noskov

备注：
The paper has been completely rewritten and differs essentially from "Constructing invariant Heine-Borel metrics for proper G-spaces". The main result extended to the more general case when $G$ is a topological group which acts properly on a locally compact $σ$-compact Hausdorff space $X$. Note that there is a gap in the proof of Theorem 2.4 of the old version
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摘要：

证明了如果一个（局部紧）群$G$适当地作用在一个局部紧$σ$ -紧空间$X$上，则存在一族$G$ -不变的适当连续有限值伪度量，它诱导了$X$的拓扑.如果$X$是进一步可度量化的，则$G$正确作用于$X$当且仅当存在$X$上的$G$不变的正确相容度规。

英文摘要：

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 $X$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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