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Tagged with sumset functional-analysis
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Is the sum of a closed unit ball and a closed set itself closed?
I am reading here that in a Banach space, the sum of the closed unit ball with a closed bounded convex set might fail to be closed itself. It seems there is a counterexample if and only if the ...
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Is the Minkowski sum of two connected sets also connected? [closed]
Is the Minkowski sum of two connected sets, $A+B$, also connected?
Can I use translation mapping here?
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Sum of closed and compact set in a TVS
I am trying to prove: $A$ compact, $B$ closed $\Rightarrow A+B = \{a+b | a\in A, b\in B\}$ closed (exercise in Rudin's Functional Analysis), where $A$ and $B$ are subsets of a topological vector space ...
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If $A$ and $B$ are compact, then so is $A+B$.
This is an exercise in Chapter 1 from Rudin's Functional Analysis.
Prove the following:
Let $X$ be a topological vector space. If $A$ and $B$ are compact subsets of $X$, so is $A+B$.
My guess: ...
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