Definition talk:Convex Set (Vector Space)

The use of putting the examples on a subpage is doubtful, since examples hardly form a proper part of the page - rather, a collection of links pointing to further pages on PW. But that's not a problem; we all have to learn and without exception we make mistakes at doing so. --Lord_Farin (talk) 19:58, 15 January 2013 (UTC)


 * What I started doing in Topology and Group Theory was set up categories of Examples, and have pages defining those examples and proving that they are indeed examples of such objects. Then it allows you to use those examples as sub-categories again, thus capturing all the results about such an object in one place. --prime mover (talk) 20:10, 15 January 2013 (UTC)


 * While topological spaces and groups may have quite a few interesting properties (being compact or simple, for example) such is not really the case for convex sets. They're just convex (admittedly, being closed or not) and do not have a huge theory about them (there is considerable work in functional analysis building on them, but as a means rather than a target). --Lord_Farin (talk) 20:14, 15 January 2013 (UTC)


 * In which case I'm with L_F and say: don't bother with a page of examples - if they are absolutely essential to the understanding put them in "Also see" but if they're just more or less interesting applications of such, there is no need to bother with this section.


 * This is the difference between ProofWiki and an encyclopedia. Pages on ProofWiki are intended to be as pithy as possible, with the minimum of indirectly relevant information, like a dictionary. --prime mover (talk) 20:47, 15 January 2013 (UTC)


 * I would say there is merit in a few well-chosen examples to help illustrate the concept and get a feel of how such structures behave. Admittedly this is not widely spread on PW at this stage, but I think it can be useful. OTOH, it's not as important as to merit a separate page - or it would be for a page with a comprehensive listing of examples and (links to) proofs. More thought is needed on how to provide this piece of infrastructure. Again, I stress that (worked) examples are one of the best ways to get familiar with a concept, so that there is merit in covering them. --Lord_Farin (talk) 20:55, 15 January 2013 (UTC)


 * Like what I just did would suit best, I think. If you have a significant amount of material of which only a part is to be shown on the parent page, then subpage and transclusion works at its best. --prime mover (talk) 21:01, 15 January 2013 (UTC)


 * Even better idea: just cite the results and remove all the excess words. --prime mover (talk) 21:50, 15 January 2013 (UTC)