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Definition: Recall that if A is a subset of a space X, the interior of A is defined as the union of all open sets of X that are contained in A. To say that A has empty interior is to say then that A contains no open set of X other than the empty set. Equivalently, A has empty interior if every point of A is a limit point of the complement of A, that is, if the complement of A is dense in X.
Source: Topology (second edition) by James R. Munkres