Talk:Convex Set Characterization (Order Theory)

We probably want to prove the equivalent of this theorem for convex sets in vector spaces. A closed convex set in that context is the intersection of closed half-spaces, and the other way 'round. It probably holds in one direction for open convex sets. --Dfeuer (talk) 22:59, 19 February 2013 (UTC)


 * Not entirely sure what you mean by that. "Half-space" seems to require some notion of "direction" (I can't imagine a half-space in a function space) which quickly leads me to Hilbert spaces. But I could be wrong. Do you have some reference on half-spaces? --Lord_Farin (talk) 08:23, 20 February 2013 (UTC)


 * Nothing in print, but there's certainly no difficulty in finite-dimensional real vector spaces. Wikipedia claims the notion applies to affine spaces, but Wikipedia can't be trusted. --Dfeuer (talk) 08:42, 20 February 2013 (UTC)


 * Not so much that it can't be trusted (although it's obvious that it can't) so much as that because it is a secondary (or is it tertiary?) resource it is important to go back to the original publications from which the material came. Document searches are so obviously your thing that we can leave it to you to do the appropriate research? --prime mover (talk) 09:02, 20 February 2013 (UTC)