I'm really stuck on this simple problem: Let X be a topological vector space and U, V are open sets in X. Prove that U+V is open.(adsbygoogle = window.adsbygoogle || []).push({});

It should be a direct consequence of the continuity of addition in topological vector spaces. But continuity states that the [tex]f^{-1}(V)[/tex] is open whenever V is open, but not the converse. It would work if I showed that adding a constant is a homeomorphism, but I don't think this is the way I should do it. Is there any more simple way, that I overlooked?

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# Simple topological problem

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