Talk:Locally convex topological vector space
Just started with the basics here (it was on Wikipedia:Requested articles/mathematics). Most of the Topological vector space article is actually on LCTVSs, so I think rather than take this page much further on its own, some material be transferred. --AndrewKepert 03:30, 11 Mar 2004 (UTC)
I've merged in the locally convex page. This leaves a couple of problems.
(1) Slight conflict in definitions to resolve (one convex nhd versus a base of such.
(2) The phrasing about all examples at topological vector space being LC is obviously not a secure thing to do.
Charles Matthews 06:57, 4 May 2004 (UTC)
Hi Charles
Yes, I agree that rationalisation between the two pages is necessary, but didn't get around to it myself. However, LCTVSs require a base of convex neighbourhoods -- otherwise every TVS is locally convex (f'rinsance, the whole space is a convex nbhd of 0). Where did you pick up that only a single nbhd was necessary - the source will need fixing. I will fix the wording here, while keeping your informal/formal characterisation.
I also agree that my note that "all examples" is dangerous, especially as I then went on to add the non-locally-convex example to the TVS page ... oh well.