Asymptotic properties of the (convex) hyperspaces
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.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2020-02-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/1605 |
| _version_ | 1818524211455459328 |
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| author | Mykhailo Zarichnyi Mykhailo Romanskyi |
| author_facet | Mykhailo Zarichnyi Mykhailo Romanskyi |
| author_sort | Mykhailo Zarichnyi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T05:54:19Z |
| format | Article |
| id | doaj.art-43c771dbc9364cf5a4a377b36cf87d5d |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-12-11T05:54:19Z |
| publishDate | 2020-02-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-43c771dbc9364cf5a4a377b36cf87d5d2022-12-22T01:18:43ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062020-02-0183-4606410.15673/tmgc.v8i3-4.16051605Asymptotic properties of the (convex) hyperspacesMykhailo Zarichnyi0Mykhailo Romanskyi1Ivan Franko National University of LvivDrohobych State Pedagogical University of Ivan FrankoIt 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.https://journals.onaft.edu.ua/index.php/geometry/article/view/1605hyperspace, convex set, coarse equivalence |
| spellingShingle | Mykhailo Zarichnyi Mykhailo Romanskyi Asymptotic properties of the (convex) hyperspaces Pracì Mìžnarodnogo Geometričnogo Centru hyperspace, convex set, coarse equivalence |
| title | Asymptotic properties of the (convex) hyperspaces |
| title_full | Asymptotic properties of the (convex) hyperspaces |
| title_fullStr | Asymptotic properties of the (convex) hyperspaces |
| title_full_unstemmed | Asymptotic properties of the (convex) hyperspaces |
| title_short | Asymptotic properties of the (convex) hyperspaces |
| title_sort | asymptotic properties of the convex hyperspaces |
| topic | hyperspace, convex set, coarse equivalence |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/1605 |
| work_keys_str_mv | AT mykhailozarichnyi asymptoticpropertiesoftheconvexhyperspaces AT mykhailoromanskyi asymptoticpropertiesoftheconvexhyperspaces |