Properties of K-Additive Set-Valued Maps

For monoids X, Y and a submonoid K ? Y we define a K additive set-valued map F : X ? 2(Y) as a map which is additive modulo K. In the paper fundamental properties of K -additive set-valued maps are studied. Among others, we prove that in the class of K -additive set valued maps K -lower (or weakly K -upper) boundedness on a large set implies K -continuity on the domain, as well as K -continuity implies K homogeneity. We also study an algebraic structure of the K -homogeneity set for K -additive set-valued maps.

Automated summary

This paper studies the fundamental properties of K-additive set-valued maps. Among other things, it is proven that K-lower (or weakly K-upper) boundedness on a large set implies K-continuity on the domain, and K-continuity implies K-homogeneity. The algebraic structure of the K-homogeneity set for K-additive set-valued maps is also examined.