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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| Видавець: | Lugansk National Taras Shevchenko University |
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| Дата: | 2021 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1485 |
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Algebra and Discrete Mathematics| id |
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oai:ojs.admjournal.luguniv.edu.ua:article-14852021-01-29T09:38:49Z Decompositions of set-valued mappings Protasov, I. set-valued mapping, selector, ballean 03E05, 54E05 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. Lugansk National Taras Shevchenko University 2021-01-29 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1485 10.12958/adm1485 Algebra and Discrete Mathematics; Vol 30, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1485/pdf Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
set-valued mapping selector ballean 03E05 54E05 |
| spellingShingle |
set-valued mapping selector ballean 03E05 54E05 Protasov, I. Decompositions of set-valued mappings |
| topic_facet |
set-valued mapping selector ballean 03E05 54E05 |
| format |
Article |
| author |
Protasov, I. |
| author_facet |
Protasov, I. |
| author_sort |
Protasov, I. |
| title |
Decompositions of set-valued mappings |
| title_short |
Decompositions of set-valued mappings |
| title_full |
Decompositions of set-valued mappings |
| title_fullStr |
Decompositions of set-valued mappings |
| title_full_unstemmed |
Decompositions of set-valued mappings |
| title_sort |
decompositions of set-valued mappings |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1485 |
| work_keys_str_mv |
AT protasovi decompositionsofsetvaluedmappings |
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2024-04-12T06:25:38Z |
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2024-04-12T06:25:38Z |
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