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locally closed∗ asteroid† 2013-03-21 23:56:53 Definition - A subset Y of a topological space X is said to be locally closed if it is the intersection of an open and a closed subset. The following result provides some equivalent definitions: Proposition - The following are equivalent: 1. Y is locally closed in X. 2. Each point in Y has an open neighborhood U ⊆ X such that U ∩ Y is closed in U (with the subspace topology). 3. Y is open in its closure Y (with the subspace topology). ∗ hLocallyClosedi created: h2013-03-21i by: hasteroidi version: h40018i Privacy setting: h1i hDefinitioni h54D99i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1