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## Diffeo/Homeo Morphisms And Dimension

Algebraic Topology
Tsakanikas Nickos
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### Diffeo/Homeo Morphisms And Dimension

Let $U$ be an open subset of $\mathbb{R}^{n}$ and let $V$ be an open subset of $\mathbb{R}^{m}$ for some $n,m \in \mathbb{N}$. Show that if $U$ and $V$ are diffeomorphic or just homeomorphic, then $n=m$.