Closeness and linkness in balleans
A set $X$ endowed with a coarse structure is called ballean or coarse space. For a ballean $(X, \mathcal{E})$, we say that two subsets $A$, $B$ of $X$ are close (linked) if there exists an entourage $E\in \mathcal{E}$ such that $A\subseteq E [B]$, $B\subseteq E[A]$ (either $A, B$ are bounded or cont...
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| Main Authors: | , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2020-03-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/9 |
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| Summary: | A set $X$ endowed with a coarse structure is called ballean or coarse space. For a ballean $(X, \mathcal{E})$, we say that two subsets $A$, $B$ of $X$ are close (linked) if there exists an entourage $E\in \mathcal{E}$ such that $A\subseteq E [B]$, $B\subseteq E[A]$ (either $A, B$ are bounded or contain unbounded close subsets). We explore the following general question: which information about a ballean is contained and can be extracted from the relations of closeness and linkness. |
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| ISSN: | 1027-4634 2411-0620 |