Talk:Hausdorff maximal principle
From Wikipedia, the free encyclopedia
 |
|||||
| Mathematics rating: | Stub Class | Low Priority | Field: Foundations, logic, and set theory | ||
| Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article. | |||||
[edit] Maximal
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)
[edit] Obvious
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)
- After you get to infinity, then what? What if, as in general topology, your partially ordered set contains an uncountable infinity of elements? linas 01:20, 8 April 2007 (UTC)
