Let $A$ be a partially ordered set in which every chain has an upper bound, and let $a \in A$. Then $A$ has a maximal element $u$ such that $u \ge a$.

score 60 · Answer 11 · 2014-08-25 18:10:26

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Understanding the notation of a response to a question about extending partial orderings.

Published on 25 Aug 2014 - 18:10

score 666 · Answer 12 · 2014-08-26 11:04:54

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score 301 · Answer 13 · 2014-08-26 22:37:37

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Homework | Prove Relation is Partial Order

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score 528 · Answer 14 · 2014-08-27 02:08:17

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score 51 · Answer 15 · 2014-08-28 12:36:58

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Is the function $x \mapsto \max\{f(x),g(x)\}$ always an automorphism if $f$ and $g$ are?

Published on 28 Aug 2014 - 12:36

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Let $A$ be a partially ordered set in which every chain has an upper bound, and let $a \in A$. Then $A$ has a maximal element $u$ such that $u \ge a$.

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