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  3. prove that every complete lattice has a unique max

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

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Advance Math

  1. Prove that every complete lattice has a unique maximalelement.

  2. (ii) Give an example of an infinite chain complete poset with nounique maximal element.

  3. (iii) Prove that any closed interval on R ([a, b]) with theusual order (?) is a complete lattice (you may assume theproperties of R that you assume in Calculus class).

  4. (iv) Say that a poset is almost chain complete if every nonemptychain has an l.u.b. Give an example of an almost chain completeposet with no minimal element.

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