(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X be an ordered set. If Y is a proper subset of X that is convex in X, does it follow that Y is an interval or a ray in X?

3. The attempt at a solution

I considered it to be yes.

Since in the ordinary situation, the assertion is obviously valid: check out the real line or the complex plane with dictionary order, in case of Y is not empty.

But I wonder if it holds when Y is an empty set or a set with only a single point.

And besides, I'm not quite sure with my own judgement, since I didn't think of any special situation (if any).

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# Homework Help: A question on Topology

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