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Suppose X {\displaystyle X} is a topological space and B {\displaystyle B} is a dense subset of X {\displaystyle X} . Suppose A {\displaystyle A} is a subset of B {\displaystyle B} that is a dense subset of B {\displaystyle B} under the subspace topology on B {\displaystyle B} from X {\displaystyle X} . Then, A {\displaystyle A} is also a dense subset of X {\displaystyle X} .
