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    Interior of a set in a topological subspace

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    Let Y be a subspace of X and let A be a subset of Y. Denote by Int_X(A) the interior of A in the topological space X and by Int_Y(A) the interior of A in the topological space Y. Prove that Int_X(A) is a subset of Int_Y(A). Illustrate by an example the fact that in general Int_X(A) not Int_Y(A).

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    Solution Summary

    The proof of the fact that the interior of a set with respect to a topological space is a subset of the interior of the same set with respect to a topoogical subset if presented. A counterxample to the general equaligy is given. The solution is in a PDF file.