Geodesic
Decompositions of set-valued mappings
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 235-238.

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Let $X$ be a set, $B_{X}$ denotes the family of all subsets of $X$ and $F\colon X \to B_{X}$ be a set-valued mapping such that $x \in F(x)$, $\sup_{x\in X} |F(x)| \kappa$, $\sup_{x\in X} |F^{-1}(x)| \kappa$ for all $x\in X$ and some infinite cardinal $\kappa$. Then there exists a family $\mathcal{F}$ of bijective selectors of $F$ such that $|\mathcal{F}|\kappa$ and $F(x) = \{ f(x)\colon f\in\mathcal{F}\}$ for each $x\in X$. We apply this result to $G$-space representations of balleans.
Keywords: set-valued mapping, selector, ballean. 
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     title = {Decompositions of set-valued mappings},
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I. Protasov. Decompositions of set-valued mappings. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 235-238. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a6/

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