Let $X$ be an infinite-dimensional normed vector space. How to construct proper convex subset $A$ of $X$, s. th. $A$ is dense in $X$ ?
If $X$ is an unitary vector space then it is obvious, but how to do it in more general case ?
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2Take the kernel of a discontinuous linear functional. – David Mitra Dec 28 '15 at 11:34
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Thanks ! It actually was obvious. :) – mikis Dec 28 '15 at 11:43
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1I wonder if it can be done without choice. – David Mitra Dec 28 '15 at 11:44