Closeness and linkness in balleans. (English) Zbl 1437.54026
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.
MSC:
| 54E99 | Topological spaces with richer structures |
| 54D80 | Special constructions of topological spaces (spaces of ultrafilters, etc.) |
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