# What is the one point compactification of $S^n\times\mathbb{R}$?

What is the one point compactification of $S^n\times \mathbb{R}$?

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I have a naive guess that it may be homotopy equivalent to $S^{n+1}\vee S^1$. – user8484 Apr 6 '11 at 14:29
Do you have a guess? Can you think of a compact space which contains a point such that its complement is homeomorphic to $S^n\times\mathbb R$? – Mariano Suárez-Alvarez Apr 6 '11 at 16:48
@user8484: are you looking for the definition of the one-point compactification? That's how I read your question. But your comment suggests you're looking for a more elementary description of the homotopy-type. – Ryan Budney Apr 6 '11 at 17:26
For example, if you had asked "what is the real numbers?" tends not to indicate the questioner is interested in a homotopy-type description. – Ryan Budney Apr 6 '11 at 17:45
$S^n\times S^1/S^n\times\{\text{pt}\}$ – yoyo Apr 6 '11 at 20:34