Mathematica Bohemica, Vol. 148, No. 2, pp. 197-210, 2023
Monotone and cone preserving mappings on posets
Ivan Chajda, Helmut Länger
Received February 25, 2021. Published online May 16, 2022.
Abstract: We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to study in which posets some of these mappings coincide. We define special mappings determined by two elements and investigate when these are strictly monotone or upper cone preserving. If the considered poset is a semilattice then its monotone mappings coincide with semilattice homomorphisms if and only if the poset is a chain. Similarly, we study posets which need not be semilattices but whose upper cones have a minimal element. We extend this investigation to posets that are direct products of chains or an ordinal sum of an antichain and a finite chain. We characterize equivalence relations induced by strongly monotone mappings and show that the quotient set of a poset by such an equivalence relation is a poset again.
Affiliations: Ivan Chajda, Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: firstname.lastname@example.org; Helmut Länger, TU Wien, Fakultät für Mathematik und Geoinformation, Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria, and Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: email@example.com