Abstract
For monoids X, Y and a submonoid Ksubset Y we define a K-additive set-valued map F:Xrightarrow 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.
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