# Prove that $\text{int}(\text{dom}(f))$ is a convex set. [closed]

Let $f$ be a convex function. I have to prove that $\text{int}(\text{dom}(f))$ is a convex set. (Be careful with $-∞$ )

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## closed as off-topic by Bookend, graydad, Adam Hughes, Micah, Zachary SelkOct 5 '15 at 4:20

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Why should he try anything? He is giving us commands. – GEdgar Oct 31 '12 at 1:33
@Stefan Thansk for your quick reply. I can prove it for function like f:$\mathbb{R}^n$U{∞} case, but not sure what will happen for -∞ case for function defined like f:$\mathbb{R}^n$ U{∞}U{-∞} – Abdul kadir Oct 31 '12 at 1:40
@GEdgar Why are you always so "reactive" with new users? – Pedro Tamaroff Oct 31 '12 at 1:43
@GEdgar Well I removed the command part :) – Abdul kadir Oct 31 '12 at 1:45
Since by the very definition of convexity $\mathop{\textrm{dom}}(f)$ is a convex set, you're basically asking how to prove that the interior of a convex set is convex? – Michael Grant Nov 22 '15 at 20:38