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For questions involving the concept of convexity

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The scalar convergence in $\mathcal{C}(X)$ is topologizable?

Let $(X,\|.\|)$ be a separable Banach space and $\mathcal{C}(X)$ be the collection of all nonempty, closed and convex subsets of $X$. For any $C$ in $\mathcal{C}(X)$ we set $$ s(x^*, C) := \sup_{x\in …
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