Explore: Continuous Lattices

complete lattices, complete join-semilattices, complete meet-semilattices, or as join-complete or meet-complete lattices. "Partial lattice" is not the

arbitrarily many two-point lattices { 0 , 1 } {\displaystyle \{0,1\}} . A continuous complete lattice is often called a continuous lattice. For a topological

defined by Dana Scott for complete lattices and later defined for arbitrary partially ordered sets. Scott-continuous functions are used in the study of

Keimel, K.; Lawson, J. D.; Mislove, M. W.; Scott, D. S. (2003). Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications. Vol

completeness properties one obtains continuous lattices and algebraic lattices, which are just complete lattices with the respective properties. For the

originally defined for lattices only. In this case, the following equivalent definition can be given: a subset I of a lattice ( P , ≤ ) {\displaystyle

properties of the underlying posets. For instance if A and B are continuous lattices, then so is the set of functions A → B with pointwise order. Using

variables may range Domain theory, the study of certain subsets of continuous lattices that provided the first denotational semantics of the lambda calculus

abelian functions. Lattices called root lattices are important in the theory of simple Lie algebras; for example, the E8 lattice is related to a Lie

Keimel, K.; Lawson, J. D.; Mislove, M. W.; Scott, D. S. (2003). Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications. Vol