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.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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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.
Transcribed Image Text: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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