Solved: Interior of set in a topological subspace, Mathematics

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Interior of set in a topological subspace

Assignment:

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) ⊂ Int_y(A). Illustrate by an example the fact that in general Int_x(A) ≠ Int_y(A).

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