Stefan Veldsman (Port Elizabeth, South Africa): Congruences on topological spaces with an application to radical theory

A fundamental notion in algebra is that of a congruence. In this talk we define a congruence on a topological space and show that it leads to topological versions of the typical algebraic notions associated with a congruence: kernels, quotients, the isomorphism theorems and subdirect representations.

As an application of the theory developed, the Hoehnke radical of a topological space can be defined as Hoehnke did for universal algebras in terms of congruences. It is shown how this ties in with the existing radical theory of topological spaces; i.e. the connectednesses and disconnectednesses as defined and developed by Arhangel'skiĭ and Wiegandt.