I was told the extended real [itex]\hat{R}=R\cup\{-\infty,\infty\}[/itex] is homeomorphic to [0,1], I was wondering if the mapping(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

h: [0,1]\rightarrow\hat{R}, h(x)=\cot^{-1}(\pi x), 0<x<1, h(0)=\infty, h(1)=-\infty

[/tex]

is a valid homeomorphism, so that a metric may be defined by the metric on [0,1]? Thank you.

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# Simple quesion about metric on extended real line

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