On Connectedness via Closure Operators

Abstract

This paper describes a convenient modification of the approach presented in the paper “Closure operators and connectedness” by G. Castellini and D. Hajek, which is shown to give a suitable generalization of left- and right-constant subcategories, both at the object and the morphism levels. We show in particular that the framework we introduce here allows the simultaneous study of the classes of connected topological spaces, of concordant continuous maps and of monotone continuous maps.