Connectedness, Disconnectedness and Closure Operators, A More General Approach

G. Castellini
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G. Castellini: University of Puerto Rico, Department of Mathematics

A chapter in Categorical Topology, 1996, pp 129-138 from Springer

Abstract: 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).

Keywords: Closure operator; Galois connection; connectedness; disconnectedness; 18A20; 18A32; 06A15 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_13

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DOI: 10.1007/978-94-009-0263-3_13

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