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first countable∗ Evandar† 2013-03-21 13:35:57 Let X be a topological space and let x ∈ X. X is said to be first countable at x if there is a sequence (Bn )n∈N of open sets such that whenever U is an open set containing x, there is n ∈ N such that x ∈ Bn ⊆ U . The space X is said to be first countable if for every x ∈ X, X is first countable at x. Remark. Equivalently, one can take each Bn in the sequence to be open neighborhood of x. ∗ hFirstCountablei created: h2013-03-21i by: hEvandari version: h32187i 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