>>14096441How do you prove that a connected subspace, U, homeomorphic to Rn, is locally dim(U)=n?
Something analogous, how do you prove a connected manifold’s dimension is the same for every x ?M?
I’m asking as a problem from Spivak. I’m actually trying to do problem 5. I have A solution, but I’m just asking here because I’m curious if anyone has something better. I seem to always have to use the fact that Rn isn’t homeomorphic to Rm for my proof, but I feel like that’s wrong. As Spivak asks that to be proved in a later exercise.
