Let $G$ be a discrete countable group and $X$ a proper (cocompact, locally-compact and hausdorff if necessary) $G$-space. Then $X$ is supposed to be second countable but I dont quite see why.
Thank you.
Proper $G$-spaces second coutable
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general-topology
group-theory
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0cocompact? what is a proper $G$-space? – 2017-02-08
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0Why is this supposed to be true? (It is not.) – 2017-02-08
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0I tried to prove this for a while. Can you provide us a counterexample? – 2017-02-08
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0$G=\{1\}$, $X$ is any Hausdorff nonmetrizable compact space. http://math.stackexchange.com/questions/74923/a-compact-hausdorff-space-that-is-not-metrizable – 2017-02-09