Abstract
AbstractFor monoids X, Y and a submonoid $$K\subset Y$$
K
⊂
Y
we define a K-additive set-valued map $$F:X\rightarrow 2^Y$$
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference10 articles.
1. Banakh, T., Gła̧b, S., Jabłońska, E., Swaczyna, J.: Haar-$${\cal{I}}$$ sets: looking at small sets in Polish groups through compact glasses. Diss. Math. 564, 1–105 (2021)
2. Banakh, T., Jabłońska, E.: Null-finite sets in metric groups and their applications. Isr. J. Math. 230, 361–386 (2019)
3. Bingham, N.H., Ostaszewski, A.J.: Normed groups: dichotomy and duality. Diss. Math. 472, 1–138 (2010)
4. Christensen, J.P.R.: On sets of Haar measure zero in abelian Polish groups. Isr. J. Math. 13, 255–260 (1972)
5. Darji, U.B.: On Haar meager sets. Topol. Appl. 160, 2396–2400 (2013)
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