A counterexample for a suptheorem in locally convex spaces
classification
🧮 math.FA
keywords
convexlocallysigmasubsetattainsboundedbriefclosed
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In this brief note, we provide an example of non complete locally convex space $E$ with a $\sigma(E, E^*)$ closed bounded subset $C\subset E$, which is not $\sigma(E, E^*)$-compact, even if every $\varphi\in E^*$ attains its sup over $C$.
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