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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]] Y 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:Topology]]
[[category: mathematics]]