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Question by Simon
Submitted on 10/9/2003
Related FAQ: N/A
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How can I prove that if X is a topological vector space, A a compact subset of X and B a closed subset of X, then A+B is closed ?
This is an exercise in Rudin's "Functional Analysis".



Answer by sanjay kumar singh
Submitted on 4/26/2007
Rating: Not yet rated Rate this answer: Vote
consider quotient space X/B with quotient topology.clearly f  : X to X/B is open map and hence proper map(inverse image of compact set is compact).f(A) is compact since A is compact and f is continous.thus A+B=inverse image of f(A) is compact.

 

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