Ivan Shishkin, Rye (1878)

Problems/TopologyExerciseUnreviewed

Un exemple simple d’homéomorphisme ?

by Ancient Tree·translated by Catalpa·
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Soit f:R→Rf:\R \rightarrow \R telle que f(x)=x+3f(x)=x+3. Est-ce un homéomorphisme?

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Solution by Anduril · translated by Catalpa

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L’application est continue et son inverse définie par g(x)=x−3g(x)=x-3, qui est aussi continue.

Expliciter l’inverse prouve que l’application est bijective.

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