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Math Help - continuity in topological spaces

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    continuity in topological spaces

    prove that if f:X->Y is continuous and if S is a subspace of X, then the restriction f|s: S->Y is continuous.

    how would i go about doing this problem? can i create a mapping from S to X, then say S is open and use the fact that f is continuous?
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    Quote Originally Posted by squarerootof2 View Post
    prove that if f:X->Y is continuous and if S is a subspace of X, then the restriction f|s: S->Y is continuous.

    how would i go about doing this problem? can i create a mapping from S to X, then say S is open and use the fact that f is continuous?
    If U is an open subset of Y then its inverse image f^{-1}(U) is open in X; and \{x\in S:f(x)\in U\} = f^{-1}(U)\cap S, which is relatively open in S. That's all there is to it!
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