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.
-- Andrew Kepert 07:16, 4 May 2004 (UTC)
- PS. I had been considering moving chunks of stuff from the TVS article to here, but on second thoughts, I don't think it (the TVS article) should be gutted. It is the most general class here, so to have an overview of everything that happens within it (all the way down to the most special, such as Hilbert spaces) is sensible. It could do with a reorganise though. -- Andrew Kepert 07:34, 4 May 2004 (UTC)
The bug with the defn was from the initial version of locally convex - a contributor only around for about a week. Charles Matthews 07:38, 4 May 2004 (UTC)