User talk:Dfeuer/Compact Subspace of Linearly Ordered Space/Converse Proof 2

Can this all be recast in terms of how the elements of the cover compare to the convex components of $Y$ in $X$? Is the so-far-untranslated part of the proof the best we can do? I suspect (based on a vague hint by Kelley) that we can make it one-sided by looking at the supremum of the set of elements whose initial segments have a finite subcover. --Dfeuer (talk) 02:07, 18 February 2013 (UTC)

Prove that $Y$ has only finitely many convex components. 2. Prove that each convex component of $Y$ is covered by a finite subset of the given cover. --04:21, 18 February 2013 (UTC)


 * Yes, the problem is that $Y$ needn't have finitely many convex components... Cantor space is compact. --Lord_Farin (talk) 08:38, 18 February 2013 (UTC)