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  • Definition: Let X be a topological space with topology T. If Y is a subset of X, the collection T_Y={Y intersect U| U is in T) is a topology on Y, called the subspace topology. With this topology, Y is called a subspace of X; its open sets consists of all intersection of open sets of X and Y.

    Source: Topology (second edition) by James R. Munkres

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