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T1 space∗ drini† 2013-03-21 13:26:22 A topological space (X, τ ) is said to be T1 (or said to hold the T1 axiom) if for all distinct points x, y ∈ X (x 6= y), there exists an open set U ∈ τ such that x ∈ U and y ∈ / U. A space being T1 is equivalent to the following statements: • For every x ∈ X, the set {x} is closed. • Every subset of X is equal to the intersection of all the open sets that contain it. • Distinct points are separated. ∗ hT1Spacei created: h2013-03-21i by: hdrinii version: h31852i Privacy setting: h1i hDefinitioni h54D10i † 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