Difference between revisions of "One-point compactification"
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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. | 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. | ||
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Revision as of 16:53, April 1, 2007
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.