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arXiv · 1911.10004

Closeness and linkness in balleans

Igor Protasov·Ksenia Protasova
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Abstract

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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Igor Protasov, Ksenia Protasova. 2019-11-22. Closeness and linkness in balleans. https://arxiv.org/abs/1911.10004

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