Difference between revisions of "One-point compactification"
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(New page: If a topological space Y is a compact, Hausdorff space; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactif...) |
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| − | If | + | If Y is a compact, [[Hausdorff space]]; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactification of X. The One-point compactification is the minimal compactification one can perform on X. A space X has a one-point compactification if and only if it is itself locally compact and Hausdorff. |
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| + | [[Category:Topology]] | ||
Latest revision as of 14:56, January 18, 2009
If Y is a compact, Hausdorff space; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactification of X. The One-point compactification is the minimal compactification one can perform on X. A space X has a one-point compactification if and only if it is itself locally compact and Hausdorff.