Difference between revisions of "Locally compact"
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A [[topological space]] X is locally compact if every point in X has a neighbourhood that is a compact subspace of X. | A [[topological space]] X is locally compact if every point in X has a neighbourhood that is a compact subspace of X. | ||
| − | '''Important Theorem''': Every locally compact Hausdorff space has a [[one-point compactification]]. | + | '''Important Theorem''': Every locally compact [[Hausdorff space]] has a [[one-point compactification]]. |
[[category: mathematics]] | [[category: mathematics]] | ||
Revision as of 04:40, March 31, 2007
A topological space X is locally compact if every point in X has a neighbourhood that is a compact subspace of X.
Important Theorem: Every locally compact Hausdorff space has a one-point compactification.