Colimits of continuous lattices

Weights of Continuous Lattices

The papers [25], [20], [1], [9], [12], [10], [22], [3], [15], [2], [23], [19], [26], [24], [27], [21], [8], [18], [5], [11], [6], [17], [16], [4], [14], and [7] provide the terminology and notation for this paper. In this article we present several logical schemes. The scheme UparrowUnion deals with a relational structure A and a unary predicate P, and states that: Let S be a family of subsets ...

Lattices of Continuous Functions

Meet – Continuous Lattices 1

The aim of this work is the formalization of Chapter 0 Section 4 of [11]. In this paper the definition of meet-continuous lattices is introduced. Theorem 4.2 and Remark 4.3 are proved. Let X, Y be non empty sets, let f be a function from X into Y , and let Z be a non empty subset of X. One can verify that f • Z is non empty. Let us note that every non empty relational structure which is reflexi...

Continuous Lattices and Domains

In order to give the book under review the right appreciation it is necessary to first say a few words about its predecessor, the monograph A Compendium of Continuous Lattices which was published by the same six authors in 1980. The Compendium, as it is commonly called, contains a rather complete and very readable account of the theory of continuous lattices as is was known by that time. It has...

Continuous approximation of binomial lattices

A systematic analysis of a continuous version of a binomial lattice, containing a real parameter γ and covering the Toda field equation as γ → ∞, is carried out in the framework of group theory. The symmetry algebra of the equation is derived. Reductions by one–dimensional and two–dimensional subalgebras of the symmetry algebra and their corresponding subgroups, yield notable field equations in...