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. | 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]]. | ||
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Latest revision as of 15:28, July 13, 2016
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.