Diffeo/Homeo Morphisms And Dimension
Posted: Fri Jun 10, 2016 7:58 pm
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 $n=m$.