first countable (original) (raw)

Let X be a topological space and let x∈X. X is said to be 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 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.