Glossary of Order Theory - B

B

• Base. See continuous poset.

• A Boolean algebra is a distributive lattice with least element 0 and greatest element 1, in which every element x has a complement ¬x, such that x ∧ ¬x = 0 and x ∨ ¬x = 1.

• A bounded poset is one that has a least element and a greatest element.

• A poset is bounded complete if every of its subsets with some upper bound also has a least such upper bound. The dual notion is not common.