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Are the polyhedral cones the only examples of cones that remains closed when they are added ...

The radial cone of $C$ is defined via $$ \mathcal R_C(x) := \bigcup_{\lambda > 0} \lambda ( C - x)$$ for all $x \in C$ and we can show $$ \mathcal R_C(x) = C + \operatorname{span}(x), $$ since $C$ is …
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