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first countable∗
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
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