Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
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Asymptotic properties of the (convex) hyperspaces

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Published Feb 13, 2020
DOI https://doi.org/10.15673/tmgc.v8i3-4.1605

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Mykhailo Zarichnyi
Ivan Franko National University of Lviv
Mykhailo Romanskyi
Drohobych State Pedagogical University of Ivan Franko

Abstract

It is  known that the hyperspaces of compact sets and compact convex set of the Euclidean space $\mathbb R^n$, $n\ge2$, both are homeomorphic to the puctured Hilbert cube.


The main result of this note states that these hyperspaces are not coarsely equivalent.

Keywords:
Hyperspace, convex set, coarse equivalence

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How to Cite
Zarichnyi, M., & Romanskyi, M. (2020). Asymptotic properties of the (convex) hyperspaces. Proceedings of the International Geometry Center, 8(3-4), 60-64. https://doi.org/10.15673/tmgc.v8i3-4.1605
Issue
Vol 8 No 3-4 (2015)
Section
Papers

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Author Biography

Mykhailo Zarichnyi, Ivan Franko National University of Lviv

Ph. D. in phys. and math.  sciences, professor, Head of the Department of Geometry and Topology of  L’viv National University named FTER Ivan Franko (Ukraine, L’viv)

References

1. D. W. Curtis, R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19--38.
2. A. N. Dranishnikov, Asymptotic topology, Uspekhi Mat. Nauk 55 (2000), no. 6(336), 71–116 (Russian); English transl., Russian Math. Surveys 55 (2000), no. 6, 1085--1129.
3. S. B. Nadler, Jr., J. Quinn and N. M. Stavrakos, Hyperspace of compact convex sets, Pacif. J. Math.{\bf 83}(1979), 441--462.
4. J. Roe, Lectures in Coarse Geometry, University Lecture Series, Vol. 31, American Mathematical Society: Providence, Rhode Island, 2003, 175pp.