Studies on Categories of Universal Topological Algebras

Abstract

<p>In this thesis we study categories of universal topological algebras and topological partially ordered sets. Topologically algebraic functors are introduced. It is shown that most of categories usually studied in general topology, universal algebras and universal topological algebras can be covered by this concept. In addition, we consider extensive subcategories of various categories of Hausdorff topological algebras and continuous homomorphisms. In particular, we obtain a method to construct extensive subcategories which is applied to categories of topological partially ordered sets and topological lattices.</p>