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Math Help - Subspace topologies

  1. #1
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    Subspace topologies

    Show that if Y is a subspace of X, and A is a subset of Y, then the topology A inherits as a subspace of Y is the same as the topology it inherits as a subspace of X.

    Since Y is a subspace, T_Y=\{Y\cap U: \ \text{U is open in X}\}

    Not sure what to do next.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Subspace topologies

    Hint As A\subset Y then A\cap (Y\cap U)=(A\cap Y)\cap U=A\cap U
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