ALL meanings of axiom of countability
ax·i·om of count·a·ble
A a - noun axiom of countability 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) 1