Oswald Wyler

Convenient categories for topology

Abstract The paper begins with a general construction of a coreflective subcategory of an epireflective subcategory of TOP. Such a category is called convenient if it is generated by a class of compact Hausdorff spaces and satisfies certain conditions, k-spaces and sequential spaces from convenient categories. It is shown that convenient categories are cartesian closed, and some consequences of this fact are obtained.

Fuzzy logic and categories of fuzzy sets

This paper deals with three topics: 1. Fuzzy logic, 2. Categories of fuzzy sets, 3. Logic of fuzzy subsets.

Algebraic Theories for Continuous Semilattices

Continuous lattices were introduced by D. Scott in [5]; they have been studied intensively and found numerous applications We refer to the Compendium [1] for a comprehensive survey of continuous lattices and related topics. In some applications, e.g. in K. Keimel’s study of compact convex sets in locally convex topological vector spaces [2], continuous sup semilattices have been useful.

Categories of Relations and Functional Relations

We define relations and their composition in a category with (e, M)-factorization structure, with M consisting of monomorphisms, but e not restricted to epimorphisms. We obtain an associativity criterion for composition of relations, and we study functional and induced relations. We show that under our assumptions, the categories of relations on functional and induced relations are isomorphic to the category of relations for the given category.

Convergence Axioms for Topology

We obtain axioms for a topology using filter convergence as the basic construct, and two very simple axioms for a topology in terms of ultrafilter convergence.