Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
We study cowellpoweredness in the category
QUnif
of quasi-uniform spaces and uniformly continuous maps. A full subcategory
A
of
QUnif
is cowellpowered when the cardinality of the codomains of any class of epimorphisms in
A
, with a fixed common domain, is bounded. We use closure operators in the sense of Dikranjan–Giuli–Tholen which provide a convenient tool for describing the subcategories
A
of
QUnif
and their epimorphisms. Some of the results are obtained by using the knowledge of closure operators, epimorphisms and cowellpoweredness of subcategories of the category
Top
of topological spaces and continuous maps. The transfer is realized by lifting these subcategories along the forgetful functor
T
:
QUnif
→
Top
and studying when epimorphisms and cowellpoweredness are preserved by the lifting. In other cases closure operators of
QUnif
are used to provide specific results for
QUnif
that have no counterpart in
Top
. This leads to a wealth of cowellpowered categories and a wealth of non-cowellpowered categories of quasi-uniform spaces, in contrast with the current situation in the case of the smaller category
Unif
of uniform spaces, where no example of a non-cowellpowered subcategory is known so far. Finally, we present our main example: a non-cowellpowered full subcategory of
QUnif
which is the intersection of two “symmetric” cowellpowered full subcategories of
QUnif
.