- #1
DavideGenoa
- 155
- 5
Dear friends, my book (an Italian language translation of Kolmogorov-Fomin's 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!
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!