Disconnectedness with respect to a closure operator
by
Gabriele Castellini
University of Puerto Rico at Mayaguez

A commutative diagram of Galois connections was previously used to introduce a notion of connectedness with respect to a closure operator in an arbitrary category X with an (E, M)-factorization structure for sinks. We ``dualize'' this approach in order to obtain a notion of disconnectedness with respect to a closure operator in the same arbitrary setting.

Under relatively mild assumptions on the category X we obtain a characterization of disconnectedness classes that in the category of topological spaces yields as a special case the one given by Arhangel'skii and Wiegandt. Moreover, in the category of abelian groups, this yields the classical characterization of the torsion free part of a torsion theory.

It is also worth to mention that in the process of obtaining the above characterization, we also identified those reflective subcategories in which the fibers of any reflection morphism have their reflections isomorphic to the terminal object.

Date received: May 29, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-19.