**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.

References:

- M.M. Clementino and W. Tholen,
*Tychonoff's Theorem in a category*,
Proc. Amer. Math. Soc. (to appear)
- M.M. Clementino, E. Giuli and W. Tholen,
*Topology in a Category: Compactness*,
Port. Math. (to appear)
- M.M. Clementino and W. Tholen,
*Separation versus Connectedness*,
preprint, Coimbra-Toronto 1996.
- D. Dikranjan and W. Tholen,
*Categorical Structure of Closure Operators, With
Applications to Topology, Algebra and Discrete Mathematics*
(Kluwer International Publishers, Dordrecht 1995)