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 $(0,∞)$ ?
2026-04-03 06:58:44.1775199524
Prove that $\mathbb{R}$ is homeomorphic to $(0,1)$
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verify that $\tan ((2x-1) \frac {\pi} 2)$ is a homeomorphism from $(0,1)$ onto $\mathbb R$.