Talk:Equivalence of Definitions of Generalized Ordered Space

Need help with transclusion approach here. I know I'm doing it wrong. --Dfeuer (talk) 08:45, 13 February 2013 (UTC)

For proofs, transclude only the Proof section. HTH. --Lord_Farin (talk) 09:14, 13 February 2013 (UTC)

The statement will have to be modified, then, to introduce the variables used. Since this thing goes in two directions, I didn't know how to do it. --Dfeuer (talk) 09:21, 13 February 2013 (UTC)

General procedure is to transclude the definitions. I already had that in a preview a few minutes back but it looks rather ugly. It motivates me to go and make work of getting the extension alive and implemented. --Lord_Farin (talk) 09:24, 13 February 2013 (UTC)

I don't know how to prove that 1 implies 2. The reason I started this page is that 2 implies 1 is needed as a lemma for the lovely proof of Compact Subspace of Linearly Ordered Space we were offered on Stackexchange, but it'd be nice to get the other direction too. --Dfeuer (talk) 16:18, 13 February 2013 (UTC)

I suspect that a proof can be crafted by adding elements to $X$ ensuring that each convex basis element is actually the intersection of (at most) two open rays. Currently busy with other things however, so I won't make a dash for it. --Lord_Farin (talk) 17:19, 13 February 2013 (UTC)

I've seen multiple references to the fact that GO-spaces can be embedded in LOTSs as dense sets or as closed sets. I'm guessing the former might use Dedekind completion, and that the latter could use a partition into convex sets as Brian Scott mentioned. --Dfeuer (talk) 17:47, 13 February 2013 (UTC)

As always, reports of references seen are not as cogent as those actual references. --prime mover (talk) 19:24, 13 February 2013 (UTC)