Hausdorff maximality theorem
The Hausdorff maximality theorem, (also called the Hausdorff maximal principle) formulated and proved by Felix Hausdorff in 1914, is an alternate formulation of Zorn's lemma and therefore also equivalent to the axiom of choice. It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset (i.e. in a totally ordered subset which, if enlarged in any way, does not remain totally ordered).
Related Topics:
Felix Hausdorff - 1914 - Zorn's lemma - Axiom of choice - Partially ordered set - Totally ordered - Subset
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
In general, there are many maximal totally ordered subsets containing a given totally ordered subset.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ Table of Content ~
| ► | Introduction |
~ What's Hot ~
The Hangover, I Love You Beth Cooper, Avatar, The Goods Live Hard Sell Hard, Daybreakers, Alvin And The Chipmunks The Squeakquel, The Boondock Saints Ii All Saints Day, Dear John, The Princess And The Frog, Sorority Row, Clash Of The Titans, Terminator 5, The Mummy 4 Rise Of The Aztec, Up In The Air, Hannah Montana The Movie, 500 Days Of Summer, New Moon, The Blind Side, Cloudy With A Chance Of Meatballs, My Sister S Keeper,
~ Community ~
| ► | History Forum Come and discuss about History, Civilizations, Historical Events and Figures |
| ► | History Web-Ring A community of sites, blogs and forums dedicated to History. Do not hesitate to submit your site. |
and are licensed under the GNU Free Documentation License.
Lexicon - Privacy Policy - Spiritus-Temporis.com ©2005.