Abstract
Let X be an arbitrary category with an (E,M)-factorization structure for sinks. A notion of constant morphism that depends on a chosen class of monomorphisms is introduced. This notion yields a Galois connection that can be seen as a generalization of the classical connectedness-disconnectedness correspondence (also called torsion-torsion free in algebraic contexts). It is shown that this Galois connection factors through the collection of all closure operators on X with respect to M).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Adamek, H. Herrlich, G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990.
G. Castellini, “Connectedness, disconnectedness and closure operators: further results,” in progress.
G. Castellini, D. Hajek, “Closure operators and connectedness,” Topology and its Appl55 (1994), 29 – 45.
G. Castellini, J. Koslowski, G.E. Strecker, “Closure operators and polarities,” Proceedings of the 1991 Summer Conference on General Topology and Applications in Honor of Mary Ellen Rudin and Her Work, Annals of the New York Academy of Sciences, Vol. 704 (1993), 38 – 52.
G. Castellini, J. Koslowski, G.E. Strecker, “An approach to a dual of regular closure operators,” Cahiers Topologie Geom. Differentielle Categoriqttes, 35 (2) (1994), 219 – 244.
M. M. Clementino, “Constant morphisms and constant subcategories,” preprint.
D. Dikranjan, E. Giuli, “Closure operators I,” Topology and its Appl27 (1987), 129 – 143.
D. Dikranjan, E. Giuli, W. Tholen, “Closure operators TI,” Proceedings of the Conference in Categorical Topology, (Prague, 1988), World Scientific (1989), 297 – 335.
M. Erné, J. Koslowski, A. Melton, G. Strecker, “A primer on Galois connections,” Proceedings of the 1991 Summer Conference on General Topology and Applications in Honor of Mary Ellen Rudin and Her Work, Annals of the New York Academy of Sciences, Vol. 704 (1993) 103 – 125.
H. Herrlich, “Topologische Reflexionen nnd Coreflexionen,” L.N.M. 78, Springer, Berlin, 1968.
D. Holgate, Closure operators in categories, Master Thesis, University of Cape Town, 1992.
M. Hušek, D. Pumplün, “Disconnectednesses,” Quaestiones Mathematicae13 (1990), 449 – 459.
J. Koslowski, “Closure operators with prescribed properties,” Category Theory and its Ap-plications(Louvain-la-Neuve, 1987) Springer L.N.M. 1248 (1988), 208 – 220.
D. Petz, “Generalized conṅectednesses and disconnectednesses in topology,” Ann, Univ. Sci. Budapest Eötvös, Sect Math24 (1981), 247 – 252.
G. Preuss, “Eine Galois-Korrespondenz in der Topologie,” Monatsh. Math75 (1971), 447 – 452.
G. Preuss, “Relative connectednesses and disconnectednesses in topological categories,” Quaestiones Mathematicae2 (1977), 297 – 306.
G. Preuss, “Connection properties in topological categories and related topics,” Springer L.N.M. 719 (1979), 293 – 305.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Castellini, G. (1996). Connectedness, Disconnectedness and Closure Operators, A More General Approach. In: Giuli, E. (eds) Categorical Topology. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0263-3_13
Download citation
DOI: https://doi.org/10.1007/978-94-009-0263-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6602-0
Online ISBN: 978-94-009-0263-3
eBook Packages: Springer Book Archive