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 contained in a compact subspace of X. | + | <nowiki>A [[topological space]] X is '''locally compact''' if every point in X has a neighbourhood that is contained in 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: Topology]] | + | [[category: Topology]]</nowiki> |
Revision as of 21:50, January 3, 2012
A [[topological space]] X is '''locally compact''' if every point in X has a neighbourhood that is contained in a compact subspace of X. '''Important Theorem''': Every locally compact [[Hausdorff space]] has a [[one-point compactification]]. [[category: Topology]]