In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability". Specifically, a space X is said to be first-countable if each point has a countable neighbourhood basis (local base). That is, for each point x in X there exists a sequence U1, U2, … of open neighbourhoods of x such that for any open neighbourhood V of x there exists an integer i with Ui contained in V.
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