Dense set
Subset whose closure is the whole space / From Wikipedia, the free encyclopedia
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In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
Formally, is dense in
if the smallest closed subset of
containing
is
itself.[1]
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The density of a topological space is the least cardinality of a dense subset of