Talk:Hausdorff maximal principle

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When is an totally ordered subset a maximal totally ordered subset? Is that when you cannot add another element without breaking total-orderedness? -- Jan Hidders 20:27 Sep 8, 2002 (UTC)

I'm guessing, but that sounds right. I would put it that no element can be added and still preserve total-orderedness. Same thing though. -- Tarquin 20:32 Sep 8, 2002 (UTC)

Yes, that's right. Note that it's not a maximally totally ordered subset (what would that even mean?), but a totally ordered subset which is maximal among the totally ordered subsets. We should probably clarify this.AxelBoldt 23:06 Sep 8, 2002 (UTC)

Why an equivalent form of the theorem is that in every partially ordered set there exists a maximal totally ordered subset is not obvious? Just start with a one element set, and extend it. Albmont 21:07, 9 December 2006 (UTC)

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