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Inverses and quotients of mappings between ordered sets
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)In: Image and Vision Computing, ISSN 0262-8856, Vol. 28, no 10, 1429-1442 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study inverses and quotients of mappings between ordered sets, in particular between complete lattices, which are analogous to inverses and quotients of positive numbers. We investigate to what extent a generalized inverse can serve as a left inverse and as a right inverse, and how an inverse of an inverse relates to the identity mapping. The generalized inverses and quotients are then used to create a convenient formalism for dilations and erosions as well as for cleistomorphisms (closure operators) and anoiktomorphisms (kernel operators).

Place, publisher, year, edition, pages
2010. Vol. 28, no 10, 1429-1442 p.
Keyword [en]
Preordered set, Complete lattice, Generalized inverse of a mapping, Division of mappings, Epigraph, Hypograph, Galois connection, Residuated mapping, Adjunction, Dilation, Erosion, Ethmomorphism, Morphological filter, Cleistomorphism, Closure operator, Anoiktomorphism, Kernel operator
National Category
URN: urn:nbn:se:uu:diva-136516DOI: 10.1016/j.imavis.2009.06.014ISI: 000280936300002OAI: oai:DiVA.org:uu-136516DiVA: diva2:377044
Available from: 2010-12-13 Created: 2010-12-13 Last updated: 2011-03-01Bibliographically approved

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Analysis and Applied Mathematics
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