Topological Invariance of Dimension

Last updated Nov 1, 2022

Let $M$ be a Nonempty Topological Manifold of Manifold Dimension $n$ and let $N$ be a Topological Manifold of Manifold Dimension $m$. If $M$ is homeomorphic to $N$, then $m=n$.

TODO - This will be done with De Rham Cohomology. See Lee - Introduction to Smooth Manifolds ch 17.