First Countability Axiom

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The first countability axiom is one of two countability axioms related to the classification of topological spaces.


A space $X$ is said to have a countable basis at $X$ if there is a countable collection $\mathscr{B}$ of neighborhoods of $X$ such that each neighborhood of $X$ contains at least one of the elements of $\mathscr{B}$. A space that has a countable basis at each of its points is said to satisfy the first countability axiom, or to be first-countable.[1]

Further Reading

See Also


  1. Munkres, James R. Topology, 2015. pg. 188.