Editing Excision theorem (section)

=== Invariance of dimension===
If nonempty open sets <math> U\subset \mathbb{R}^n</math> and <math> V\subset \mathbb{R}^m</math>
are homeomorphic, then ''m'' = ''n''. This follows from the excision theorem, the long exact sequence for the pair <math>(\mathbb{R}^n,\mathbb{R}^n-x)</math>, and the fact that <math> \mathbb{R}^n-x</math> deformation retracts onto a sphere.
In particular, <math>\mathbb{R}^n</math> is not homeomorphic to <math>\mathbb{R}^m</math> if <math>m\neq n</math>.<ref>See Hatcher 2002, p.135</ref>