first axiom of countability

noun Mathematics.

1. See under axiom of countability.

noun Mathematics.

1. the property satisfied by a topological space in which the neighborhood system of each point has a base consisting of a countable number of neighborhoods (first axiom of countability) or the property satisfied by a topological space that has a base for its topology consisting of a countable number of subsets of the space (second axiom of countability).