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. | 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. | ||
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| + | One-point compactification is the minimal compactification one can perform on X. | ||
[[category: mathematics]] | [[category: mathematics]] | ||
Revision as of 03:59, March 21, 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.
One-point compactification is the minimal compactification one can perform on X.