Timeline for The weakest condition guarantees some Separation-type of convex sets in Banach spaces
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| Jun 24, 2017 at 14:35 | comment | added | Wlod AA | Ashkan, very true. Nevertheless, starting with two disjoint non-empty convex sets which have non-empty interiors (plus perhaps some extra conditions) one could try to prove that the closures of the separating half-spaces intersect in a codimension 1 hyperplane. You could add additional specific conjectures along this line which would expand on your question providing more detailed "subquestions". Etc. (Thank you for your generous +1). | |
| Jun 24, 2017 at 8:33 | comment | added | Red shoes | Thank you very much for your answer(+1). Actually in separation for LCTV the important thing is separating disjoint convex sets through CONTINUOUS linear function, that leads us to get good result . Other wise any two convex set in a vector space can be separated by two disjoint maximal convex set which make a partition for X, so they are actually two sides of a half- space. But I am looking for a continuous separation ! | |
| Jun 24, 2017 at 7:40 | history | answered | Wlod AA | CC BY-SA 3.0 |