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Topological equivalence of an interval and the real line

Prove that the open interval (-pi/2,pi/2) considered as a subspace of the real number system, topologically equivalent to the real number system.
Prove that any two open intervals, considered as subspaces of the real number system, are topologically equivalent.
Prove that any open interval, considered as a subspace of the real number system, is topologically equivalent to the real number system.

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Two topological spaces X and Y are topologically equivalent if thereis a homeomorphism between them, that is, a continuous bijective map f: X -> ...

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The proof of the topological equivalence of an interval in the real line and the real line itself is given

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