In general topology, a topological space X is said to be first countable, or satisfy the first axiom of countability, if every point x in X has a countable neighborhood base, that is, a countable family {U(x,n)} of neighborhoods of x, such that every neighborhood of x contains one of the U(x,n). Weaker than second countable. Every metric space is first countable, since the open balls B(x, 1/n) form a neighborhood base at x. Generally spaces which are not first countable are fairly difficult to work with.

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