Lattices of continuous functions

Lattices of Continuous Functions

Completion of Lattices of Semi-continuous Functions

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

Noncommutative Lattices and the Algebras of Their Continuous Functions

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for the...

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 ...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.