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Linearly Ordered Coarse Spaces

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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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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Department of Computer Science and Cybernetics, Kyiv, Ukraine

    Igor Protasov

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  1. Igor Protasov
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Correspondence to Igor Protasov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 3, pp. 426–433, July–September, 2022.

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Protasov, I. Linearly Ordered Coarse Spaces. J Math Sci 268, 233–238 (2022). https://doi.org/10.1007/s10958-022-06194-z

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  • DOI: https://doi.org/10.1007/s10958-022-06194-z

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