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High Quality Content by WIKIPEDIA articles! In topology, a second-countable space is a topological space satisfying the "second axiom of countability". Specifically, a space is said to be second-countable if its topology has a countable base. Like other countability axioms, the property of being second-countable restricts the number of open sets that a space can have. Most "wel-behaved" spaces in mathematics are second-countable. For example, Euclidean space (Rn) with its usual topology is second-countable. Although the usual base of open balls is not countable, one can restrict to the set of all open balls with rational radii and whose centers have rational coordinates. This restricted set is countable and still forms a base.