First-countable space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

Symbol-free definition

A topological space is said to be first-countable if for any point, there is a countable basis at that point.

Definition with symbols

A topological space $X$ is said to be first-countable if for any $x\in X$, there exists a countable collection ,math>U_n</math> of open sets around $x$ such that any open $V\ni x$ contains some $U_n$.

Relation with other properties

Stronger properties

• Second-countable space

Weaker properties

• Sequential space