Dear friends, my book (an Italian language translation of Kolmogorov-Fomin's(adsbygoogle = window.adsbygoogle || []).push({}); Элементы теории функций и функционального анализа) proves the following separation theorem:let ##A## and ##B## be convex sets of a normed space and let ##A## have a non-empty algebraic interior ##J(A)## such that ##J(A)\cap B =\emptyset##. Then there is a non-null continuous linear functional separating ##A## and ##B##.

Then, with some translation errors or misprints, it says that the theorem can be generalized to locally convex topological linear spaces (Kolmogorov and Fomin don't require them to be ##T_1##). If ##A## is open I easily see that it applies, but I wonder whether it can be generalized as it is stated and hope I can find a proof of it if it can...

##\infty## thanks for any help!

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# A separation theorem in locally convex spaces

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