Prove that every complete lattice has a unique maximal element. (ii) Give an example of an...

Prove that every complete lattice has a unique maximal element.
(ii) Give an example of an infinite chain complete poset with no unique maximal element.
(iii) Prove that any closed interval on R ([a, b]) with the usual order (≤) is a complete lattice (you may assume the properties of R that you assume in Calculus class).
(iv) Say that a poset is almost chain complete if every nonempty chain has an l.u.b. Give an example of an almost chain complete poset with no minimal element.

Expert Solution

Colby Messinger answered 2 years ago

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