# First Countability Axiom

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

## Definition

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]

## References

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