Let X be a topological space, and let Y C X have the subspace topology. Prove that C C Y is closed in Y if and only if C = DnY for some closed set D in X.

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Let \( X \) be a topological space, and let \( Y \subset X \) have the subspace topology. Prove that \( C \subset Y \) is closed in \( Y \) if and only if \( C = D \cap Y \) for some closed set \( D \) in \( X \).
Transcribed Image Text:Let \( X \) be a topological space, and let \( Y \subset X \) have the subspace topology. Prove that \( C \subset Y \) is closed in \( Y \) if and only if \( C = D \cap Y \) for some closed set \( D \) in \( X \).
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