Congruences on topological spaces with an application to radical theory

A congruence is defined on a topological space. This leads to the topological versions of the algebraic isomorphism theorems and some of their consequences. In addition, a Hoehnke radical of a topological space is defined as a congruence on the space and it is shown how this ties in with the existing radical theory of topological spaces (i.e., the theory of connectednesses and disconnectednesses).