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An extension of the Rådström cancellation theorem to cornets

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AbstractThe aim of this paper is to introduce the notion of cornets, which form a particular subclass of ordered semigroups also equipped with a multiplication by natural numbers. The most important standard examples for cornets are the families of the nonempty subsets and the nonempty fuzzy subsets of a vector space. In a cornet, the convexity, nonnegativity, Archimedean property, boundedness, closedness of an element can be defined naturally. The basic properties related to these notions are established. The main result extends the Cancellation Principle discovered by Rådström in 1952.
Springer Science and Business Media LLC
Title: An extension of the Rådström cancellation theorem to cornets
Description:
AbstractThe aim of this paper is to introduce the notion of cornets, which form a particular subclass of ordered semigroups also equipped with a multiplication by natural numbers.
The most important standard examples for cornets are the families of the nonempty subsets and the nonempty fuzzy subsets of a vector space.
In a cornet, the convexity, nonnegativity, Archimedean property, boundedness, closedness of an element can be defined naturally.
The basic properties related to these notions are established.
The main result extends the Cancellation Principle discovered by Rådström in 1952.

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