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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general-topology
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0I have a naive guess that it may be homotopy equivalent to $S^{n+1}\vee S^1$. – 2011-04-06
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4Do you have a guess? Can you think of a compact space which contains a point such that its complement is homeomorphic to $S^n\times\mathbb R$? – 2011-04-06
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3@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. – 2011-04-06
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0For example, if you had asked "what is the real numbers?" tends not to indicate the questioner is interested in a homotopy-type description. – 2011-04-06
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3$S^n\times S^1/S^n\times\{\text{pt}\}$ – 2011-04-06