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.
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cocompact? what is a proper $G$-space? – Henno Brandsma Feb 08 '17 at 16:28
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Why is this supposed to be true? (It is not.) – Moishe Kohan Feb 08 '17 at 19:13
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I tried to prove this for a while. Can you provide us a counterexample? – EQJ Feb 08 '17 at 19:39
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$G={1}$, $X$ is any Hausdorff nonmetrizable compact space. http://math.stackexchange.com/questions/74923/a-compact-hausdorff-space-that-is-not-metrizable – Moishe Kohan Feb 09 '17 at 01:23