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axiom of countability

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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).
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Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018