Talk:Connected Subspace of Linearly Ordered Space

From ProofWiki
Jump to navigation Jump to search

Might it be worth starting to talk about a "totally ordered space" in the titles of pages based on this topology? It's the specific (non-trivial) topology that has been imposed on the toset which makes it what it is, after all, and just referring to the underlying set is missing all the good stuff. --prime mover (talk) 06:03, 26 October 2012 (UTC)

That's a good suggestion IMO. As always, there is a mountain of results and properties for this concept that are probably scattered throughout the literature. Do you have a reference or did this sprout from your own mind? --Lord_Farin (talk) 08:18, 26 October 2012 (UTC)
I think it's a good idea. After a quick Google search, it seems like "linearly ordered space" is the term used for this concept, while "totally ordered space" refers to something more general.
As for the question of whether I made up this page or not, the proof of this is almost identical to that of Subset of Real Numbers is Interval iff Connected. --abcxyz (talk) 15:35, 26 October 2012 (UTC)
It's in 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) as counterexample $39$: Order Topology (except you don't have to indirect twice to get a definition). They don't actually call the space anything: they just refer to the "Order Topology" but mention it's on a "linearly ordered space". I'm happy with "Linearly Ordered Space" as the generic name for this concept. --prime mover (talk) 20:01, 26 October 2012 (UTC)