# Talk:Connected Subspace of Linearly Ordered Space

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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)

- It's in 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: