Prove that $\mathbb{R}$ is homeomorphic to $(0,1)$ and that $(0,1)$ is homeomorphic to $(0, ∞)$. also is $\mathbb{R}$ isometric to $(0,1)$? to $(0,∞)$ ?
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https://math.stackexchange.com/questions/242873/homeomorphism-of-the-real-line-topology – 1123581321 Sep 27 '18 at 05:47
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I just don't know how to approach when proving homeomorphisms – Loaf Sep 27 '18 at 05:50
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2You start by finding a nice bijection. Then you prove that it is a homeomorphism. – Arthur Sep 27 '18 at 05:57
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verify that $\tan ((2x-1) \frac {\pi} 2)$ is a homeomorphism from $(0,1)$ onto $\mathbb R$.
Kavi Rama Murthy
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