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**Richard** Given a Euclidean n-space, take any compact convex set $\displaystyle S$ in that space, with a distinguished point $\displaystyle p$ in its interior. Let $\displaystyle \lambda$ be any positive real, and let $\displaystyle S^{\prime}$ be the result of scaling $\displaystyle S$ as centered on $\displaystyle p$ by the factor $\displaystyle \lambda$. I would have thought that $\displaystyle S^{\prime}$ must be compact and convex as well. However, I didn't manage prove this. Is there any easy proof for this?