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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 Live Forever, graydad, Adam Hughes, Micah, avid19 Oct 5 '15 at 4:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Live Forever, graydad, Adam Hughes, Micah, avid19
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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