On connectedness and disconnectedness
Abstract:Constant subcategories, in particular connectednesses/disconnectednesses
and torsion/ torsion-free subcategories, have been largely
investigated, namely by Dickson, Preuss,
Arhangel'skii and Wiegandt, Tiller, Tholen, Cassidy, Hebert and Kelly, Husek and
Pumplun and Clementino.
In almost all these papers, the goal is the study of some of the
particular cases referred to above.
A significant part of the results obtained there may be obtained in a
unified way, as was shown by Tiller, Tholen and Clementino,
among others.
In this paper we formulate and investigate, in a general setting, the
properties used by Arhangel'skii and Wiegandt to
characterize connectednesses and disconnectednesses in the category of
topological spaces.
This enables us to unify characterizations of constant subcategories
established in different contexts.
