A counterexample for a suptheorem in locally convex spaces

Abstract

In this brief note, we provide an example of non complete locally convex space $E$ with a $\sigma (E,E^{\ast })$ closed bounded subset $C\subset E$, which is not $\sigma (E,E^{\ast })$-compact, even if every $\phi \in E^{\ast }$ attains its sup over $C$.

3 pages