Inverses and quotients of mappings between ordered sets

• 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).

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

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

MATHEMATICS

MATEMATIK

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