a proof $\mathbb R^n$ is not homeomorphic to $\mathbb{R^m}$ without algebraic topology

Asked Jul 07 '14 at 03:20

Active Jul 07 '14 at 03:21

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i'm looking for such a proof. There is a proof of Luroth for n=1,2,3 without any topological concepts,but only analysis.(which is simple for n=1,and gets much more complicated for n=2,3)

a heard Brouwer himself prooved it even before the fixed point theorem,so the best will be if someone knows where to find it.

edited Jul 07 '14 at 03:21

J126

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asked Jul 07 '14 at 03:20

user160823

2

You might like the answer(s) given here: http://math.stackexchange.com/questions/24873/elementary-proof-that-mathbbrn-is-not-homeomorphic-to-mathbbrm?rq=1 – Mark B Jul 07 '14 at 03:42

a proof $\mathbb R^n$ is not homeomorphic to $\mathbb{R^m}$ without algebraic topology

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