Large sources and closure operators in topological constructs (Q1313220)

This paper is a contribution to the question: How to use categorical methods in the case of non-cowellpoweredness? It is focused on classes of morphisms/conglomerates of sources usually appearing as parts of a factorization structure. Large extremal monosources are characterized and investigated. An example of a source in the category of Urysohn spaces is given, having no (Epi, Extremal Monosource)-factorization. Results of \textit{H. Lord} [(\(A\)-epi, \(M_ A\))-factorization structures in TOP, in ``Categorical topology and its relation to analysis, algebra and combinatorics'', Proc. Conf. Categorical Topology, Prague 1988, World Scientific, Singapore, 95-119 (1989)] and \textit{D. Dikranjan} and \textit{E. Giuli} [Closure operators. I. Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)] and \textit{D. Dikranjan, E. Giuli} and \textit{W. Tholen} [Closure operators. II, in: Cat. Top. Prague 1988 (see above), 297-335 (1989)] are unified. A new non-cowellpowered category is exhibited, using a method of \textit{D. Pumplün} and \textit{H. Röhrl} [Separated totally convex spaces, Manuscr. Math. 50, 145-183 (1985; Zbl 0594.46064)].