Closure operators -- a link between algebra and topology

Walter Tholen
Department of Mathematics and Statistics
York University

A categorical closure operator of a suitably structured category provides the subobject lattice of each object with a closure operation such that every morphism becomes ``continuous''. This topologically-motivated concept finds its examples not only in topology but also in algebra and lattice theory, especially in module theory. In this talk, we wish to outline a categorical theory of seperation, compactness and connectedness, which is strong enough to entail the classical product theorems of topology and other results, and general enough to allow for interesting algebraic applications.