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Results tagged with homogeneous-spaces
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user 3969
6
votes
For $\mathbb R^n \times Q \cong \mathbb R^m \times Q $ must $n = m$? ($Q$ is the Hilbert cube)
Note that $\mathbb{R}^n\times Q$ is proper homotopy equivalent to $\mathbb{R}^n$.
If they were homeomorphic, we would obtain a proper homotopy equivalence between $\mathbb{R}^m$ and $\mathbb{R}^n$.
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