Decompositions of set-valued mappings
Let \(X\) be a set, \(B_{X}\) denotes the family of all subsets of \(X\) and \(F: X \to B_{X}\) 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 the...
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| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1485 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(X\) be a set, \(B_{X}\) denotes the family of all subsets of \(X\) and \(F: X \to B_{X}\) 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 \(F(x) = \{ f(x): f\in\mathcal{F}\}\) for each \(x\in X\). We apply this result to \(G\)-space representations of balleans. |
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