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Math Help - Subspace topology

  1. #1
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    Subspace topology

    Let X be a topological space, and let Y subset of X have the subspace topology.
    (a) If A is open in Y, and Y is open in X, show that A is open in X.
    (b) If A is closed in Y, and Y is closed in X, show that A is closed in X.
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  2. #2
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    Quote Originally Posted by horowitz View Post
    Let X be a topological space, and let Y subset of X have the subspace topology.
    (a) If A is open in Y, and Y is open in X, show that A is open in X.
    (b) If A is closed in Y, and Y is closed in X, show that A is closed in X.
    (a) If A is open in Y, then A=Y \cap U for an open set U in X by the definition of a subspace topology. An intersection of open sets is an open. Thus, A is open in X.

    (b) is similar to (a).
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