Elementary proof that $Gl_n(\mathbb R)$ and $Gl_m(R)$ are homeomorphic iff $n=m$

This question already has an answer here:

  • Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$

    6 answers

Solutions Collecting From Web of "Elementary proof that $Gl_n(\mathbb R)$ and $Gl_m(R)$ are homeomorphic iff $n=m$"