Linearly ordered coarse spaces

DOI10.1007/S10958-022-06194-ZarXiv2110.01377MaRDI QIDQ6379315

Igor V. Protasov

Publication date: 10 September 2021

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.

Mathematics Subject Classification ID

Continuous maps (54C05) Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Dimension theory in general topology (54F45)

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