Compactness with respect to a convergence structure
by
Josef Slapal
Technical University of Brno

A convergence structure for a category is given by determining convergent nets and their limits for each object of this category under validity of some basic convergence axioms. The nets considered are obtained as a categorical generalization of the usual nets. A convergence structure for a category is, under some natural conditions, a closure operator of the category. We study separatedness and compactness of objects of a given category with respect to a convergence structure and show that they behave more naturally than separatedness and compactness with respect to a closure operator.

Date received: May 30, 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-22.