I am curious about the following statement :
Statement : Infinite connected sum of $S^n$ is homeomorphic to $\mathbb{R}^n.$
Any hint, proof of reference will be appreciated.
Thank you.
2025-01-13 00:13:12.1736727192
Infinite connected sum of S^n
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Think of a nested countable sequence of $(n-1)$-spheres in $\mathbb R^n$ starting with the unit sphere and going out to $\infty$. The annuli between each sphere are homeomorphic to $S^n$ with two disks removed. So this realizes the infinite connected sum.