Linearly ordered coarse spaces

Igor Protasov

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arXiv · 2110.01377

Linearly ordered coarse spaces

Igor Protasov

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Abstract

A coarse space $X$, endowed with a linear order compatible with the coarse structure of $X$, is called linearly ordered. We prove that every linearly ordered coarse space $X$ is locally convex and the asymptotic dimension of $X$ is either $0$ or $1$. If $X$ is metrizable then the family of all right bounded subsets of $X$ has a selector.

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BibTeX RIS

Igor Protasov. 2021-09-10. Linearly ordered coarse spaces. https://arxiv.org/abs/2110.01377

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