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Aug 5, 2022 at 17:43 history edited Toni Mhax CC BY-SA 4.0
Clarification
Aug 5, 2022 at 16:11 comment added Piku I am very sorry that I forgot to mention $S\subseteq\{z\in\mathbb{C}:\vert z\vert=1\}$ is a compact set such that $\text{conv} S\supseteq\{z\in\mathbb{C}:\vert z\vert\leq\frac{1}{\sqrt{2}}\}$. But I accept that your example answers the question that I have asked in negative.
Aug 5, 2022 at 14:59 history edited Toni Mhax CC BY-SA 4.0
added 1 character in body
Aug 5, 2022 at 13:04 history answered Toni Mhax CC BY-SA 4.0