Forgot one condition on (X,d)

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edited Oct 24, 2016 at 2:45

Let $(X,d)$ be a complete separable metric space, and endow $Iso(X,d)$ with the pointwise convergence topology.

I've seen a few sources say this is clearly a Polish group, but why is this this the case?

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edited Oct 24, 2016 at 0:32

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asked Oct 24, 2016 at 0:27

Isometry group of a complete separable metric space is Polish?

Let $(X,d)$ be a complete metric space, and endow $Iso(X,d)$ with the pointwise convergence topology.

I've seen a few sources say this is clearly a Polish group, but why is this this the case?

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