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Aug 11, 2020 at 18:29 vote accept erz
Aug 11, 2020 at 17:28 answer added Jochen Wengenroth timeline score: 1
Aug 11, 2020 at 16:41 comment added erz @JochenWengenroth yeah, perhaps I should have put this example in the question itself. Luckily (?), in my situation I have additional convexity assumption
Aug 11, 2020 at 16:11 comment added Jochen Wengenroth Without convexity a counterexample would be $X=\mathbb R$ and $B=\{f_n:n\in\mathbb N\} \cup\{1\}$ where $f_n$ are $1$ outside $(0,2/n)$, $f_n(1/n)=0$ and affine linear and on the two halfs of $[0,2/n]$ so that they are continuous. Then $f_n\to 1$ pointwise which implies compactness.
Aug 11, 2020 at 14:31 history asked erz CC BY-SA 4.0