Talk:Linear space (geometry)

Third axiom (2009)

I just realized that my last edit disagrees with the third axiom listed defining linear spaces. However, I will leave it for now because a linear space has been defined for me to not include the third axiom. My source is, among others, the 1997 paper "Linear Spaces with at Most 12 Points" by Betten and Betten. Sillcat (talk) 17:16, 17 February 2008 (UTC)

Apparently the definition of the linear space varies in literature, some use the 3rd axiom others don't. One of the references in the article (beutelspacher) writes: Quite often the 3rd axiom is dropped when defining a linear space. In that case the linear spaces with at least 2 lines are considered nontrivial, since the trival linear spaces are easy to classify, we want to exclude them from the start.--Kmhkmh (talk) 10:17, 9 January 2009 (UTC)

Merge suggestion

The main content of this article essentially duplicates the incidence geometry article, but it would be nice if some things could be salvaged from this article for the other.Rschwieb (talk) 00:27, 14 November 2013 (UTC)

Actually it is the other way around, the article for incidence geometry duplicated much of the content here, which unfortunately turns the incidence geometry article in an article about linear spaces for the most part, that however is mostly a problem of that article, which needs to be extended into an overview article about incidence spaces rather than just dealing with linear spaces.

In any case the subjects need their own articles anyhow (at least in the long run), so merging makes little sense here. The relation between linear space and incidence geometry is like the relation between group and algebra, that is the latter gives a short summary coverage of the former but 2 separate articles are needed.--Kmhkmh (talk) 02:05, 14 November 2013 (UTC)

Ahh, earlier I had fooled myself into thinking that what was being described here was just a synthetic development of affine planes, but now I see that these are even more general. Given that relationship with the two articles, I am definitely happy to concede this article's independence. I guess all that's left is to check that any needless duplication is smoothed out, and then we have an acceptable structure. Rschwieb (talk) 17:34, 14 November 2013 (UTC)

Yes affine spaces are a special case of linear spaces. I agree that the redundancy of both articles could be reduced bit in particular incidence geometry needs to be turned into a real overview article on the subject rather than being an introduction into linear spaces.--Kmhkmh (talk) 00:41, 15 November 2013 (UTC)