Closeness and linkness in balleans

I.V. Protasov; K. Protasova

doi:10.30970/ms.53.1.100-108

I.V. Protasov Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
K. Protasova Faculty of Computer Science and Cybernetics Kyiv University

DOI: https://doi.org/10.30970/ms.53.1.100-108

Keywords: Coarse structure; ballean; coarse space; closeness; linkness; rigidity; stability

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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