Definition talk:Vector Subspace

Looks like there is a need for the page Definition:Linear Manifold to define the concept of a closed linear subspace? --prime mover 09:50, 17 December 2011 (CST)
 * You may have misunderstood. A linear manifold is what is defined here as a linear subspace. Then, a linear subspace is meant to be inherently closed. I have adapted the statement for clarity. --Lord_Farin 09:55, 17 December 2011 (CST)
 * Having done that, I want to point out that it is less ambiguous to write closed linear subspace every time Conway (my source for this terminology) writes linear subspace. --Lord_Farin 09:58, 17 December 2011 (CST)
 * I wouldn't have a problem with renaming this page "linear manifold" (along with some associated rewording), then adding a new page "linear subspace" to define "closed linear manifold". The name "vector subspace" can still sit there with a redirect. My source work (Warner) is, I have been informed, unusual in its terminology and symbology, so I'm more than happy to defer to a more mainstream set of definitions etc. --prime mover 17:19, 17 December 2011 (CST)
 * Mainstream terminology is better, indeed. However I haven't encountered 'linear manifold' outside Conway, and hence am quite reluctant to let it prevail. Other opinions/references on this? --Lord_Farin 02:25, 19 December 2011 (CST)

When $T$ is a closed subset of $S$, isn't it automatically a $K$-vector space? --Lord_Farin 03:49, 3 February 2012 (EST)