Abstract
Given a coarse space (X; 𝜀), we consider linear orders on X compatible with the coarse structure 𝜀 and explore interplays between these orders and macro-uniform selectors of (X; 𝜀).
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T. Banakh, I. Protasov, D. Repovs, and S. Slobodianiuk, “Classifying homogeneous cellular ordinal balleans up to coarse equivalence,” Colloquium Mathematicum, 149, 211–224 (2017).
T. Banakh and I. Zarichnyi, “Characterizing the Cantor bi-cube in asymptotic categories,” Groups Geom. Dynam., 5, 691–728 (2011).
Y. Cornulier and P. de la Harpe, “Metric geometry of locally compact groups,” Colloquium Mathematic in Mathematics, 25, Zürich (2016).
D. Dikranjan, I. Protasov, K. Protasova, and N. Zava, “Balleans, hyperballeans and ideals,” Appl. Gen. Topology, 2, 431–447 (2019).
P. de la Harpe, Topics in Geometrical Group Theory. University Chicago Press (2000).
I. V. Protasov, “Morphisms of ball’s structures of groups and graphs,” Ukrain. Mat. Zh., 54, 847–855 (2008).
I. V. Protasov, “Balleans of bounded geometry and G-spaces,” Algebra Discrete Math., 7(2), 101–108 (2008).
I. Protasov, “Selectors of discrete coarse spaces,” Comment.Math. Univ. Carolin. preprint arXiv: 2101.07199 (to appear).
I. Protasov and T. Banakh, Ball Structures and Colorings of Groups and Graphs. Math. Stud. Monogr. Ser., vol. 11. VNTL, Lviv (2003).
I. Protasov and K. Protasova, “On hyperballeans of bounded geometry,” Europ. J. Math., 4, 1515–1520 (2018).
I. Protasov and K. Protasova, “The normality of macrocubes and hiperballeans,” Europ. J. Math. (2020). https://doi.org/10.1007/s40879-020-00400-x.
I. Protasov and M. Zarichnyi, General Asymptology. Math. Stud. Monogr. Ser., vol. 12. VNTL, Lviv (2007).
J. Roe, Lectures on Coarse Geometry. Univ. Lecture Ser., vol. 31. American Mathematical Society, Providence RI (2003).
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Translated from Ukrains’kiÄ MatematychnyÄ Visnyk, Vol. 18, No. 1, pp. 71–79, January–March, 2021.
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Protasov, I. Selectors and orderings of coarse spaces. J Math Sci 256, 779–784 (2021). https://doi.org/10.1007/s10958-021-05460-w
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DOI: https://doi.org/10.1007/s10958-021-05460-w