All Questions
Tagged with sumset topological-vector-spaces
3
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Does $\overline{A+B}=\overline A+\overline B$ hold if $\overline A$ and $\overline B$ are compact?
Let us assume that we are working with subsets $A$, $B$ of some topological space $X$ such that also $A+B$ makes sense. (For example, we can have $X=\mathbb R^n$, $X$ could be a topological group, a ...
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22
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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 ...
- 911
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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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