first countable

Let X be a topological spaceMathworldPlanetmath and let xX. X is said to be at x if there is a sequence (Bn)n of open sets such that whenever U is an open set containing x, there is n such that xBnU.

The space X is said to be if for every xX, X is first countable at x.

Remark. Equivalently, one can take each Bn in the sequence to be open neighborhood of x.

Title first countable
Canonical name FirstCountable
Date of creation 2013-03-22 12:23:33
Last modified on 2013-03-22 12:23:33
Owner Evandar (27)
Last modified by Evandar (27)
Numerical id 5
Author Evandar (27)
Entry type Definition
Classification msc 54D99
Synonym first axiom of countability
Related topic SecondCountable
Related topic TestingForContinuityViaNets