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Meaning of axiom of countability

ax'iom of countabil'ity

Pronunciation: [key]
— Math. Math.
  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 neighborhoodsor the property satisfied by a topological space that has a base for its topology consisting of a countable number of subsets of the space
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.