NDLI: On Partially Ordered Semigroups and an Abstract Set-Difference

Content Provider	Springer Nature Link
Author	Pallaschke, D. Przybycień, H. Urbański, R.
Copyright Year	2008
Abstract	In this paper we prove the independence of a system of five axioms (S1)–(S5), which was proposed in the book of Pallaschke and Urbański (Pairs of Compact Convex Sets, vol. 548, Kluwer Academic Publishers, Dordrecht, 2002) for partially ordered commutative semigroups. These five axioms (S1)–(S5) are stated in the introduction below. A partially ordered commutative semigroup satisfying these axioms is called a F-semigroup. By the use of a further axiom (S6) we define an abstract difference for the elements of a F-semigroup and prove some basic properties. The most interesting example of a F-semigroup are the nonempty compact convex sets of a topological vector space endowed with the Minkowski sum as operation and the inclusion as partial order. In Section 4 we apply the abstract difference to the problem of minimality of convex fractions.
Starting Page	257
Ending Page	265
Page Count	9
File Format	PDF
ISSN	09276947
Journal	Set-Valued Analysis
Volume Number	16
Issue Number	2-3
e-ISSN	1572932X
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-03-04
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Convex analysis Pairs of compact convex sets Semi-groups Commutative semigroups Convex sets in topological vector spaces Nonsmooth analysis Geometry Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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