Categorical closure operators via Galois connections. (English) Zbl 0793.18001

Castellini, G.; Koslowski, J.; Strecker, George E.

Gähler, Werner (ed.) et al., Recent developments of general topology and its applications. International conference in memory of Felix Hausdorff (1868 - 1942), held in Berlin, Germany, March 22-28, 1992. Berlin: Akademie-Verlag. Math. Res. 67, 72-79 (1992).

Closure operators [in the sense introduced by E. Giuli and the reviewer, Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)] are considered as fixed points of a Galois connection. As an application a factorization of the Plumpün-Röhrl connection [D. Pumplün and H. Röhrl, Manuscr. Math. 50, 145-183 (1985; Zbl 0594.46064)] is obtained [see also the authors’ previous paper, Topology Appl. 44, 69-76 (1992; Zbl 0774.18002)].
For the entire collection see [Zbl 0781.00012].

Reviewer: D.Dikranyan (Udine)

MSC:

18A99	General theory of categories and functors
06A15	Galois correspondences, closure operators (in relation to ordered sets)
18A32	Factorization systems, substructures, quotient structures, congruences, amalgams

Keywords:

closure operators; fixed points; Galois connection; Plumpün-Röhrl connection

Citations:

Zbl 0634.54008; Zbl 0594.46064; Zbl 0774.18002

Software:

PLUMP