Intermediate-value property for Assouad dimension by its inversion invariance
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Luukkainen , J 2021 , ' Intermediate-value property for Assouad dimension by its inversion invariance ' , Topology and Its Applications , vol. 297 , 107700 , pp. 1-2 . https://doi.org/10.1016/j.topol.2021.107700
| Title: | Intermediate-value property for Assouad dimension by its inversion invariance |
| Author: | Luukkainen, Jouni |
| Contributor organization: | Department of Mathematics and Statistics |
| Date: | 2021-06-15 |
| Language: | eng |
| Number of pages: | 2 |
| Belongs to series: | Topology and Its Applications |
| ISSN: | 0166-8641 |
| DOI: | https://doi.org/10.1016/j.topol.2021.107700 |
| URI: | http://hdl.handle.net/10138/329617 |
| Abstract: | We prove that if X is a metric space of Assouad dimension s is an element of (0, infinity), then for every alpha is an element of [0, s] there is a countable subset of X of Assouad dimension alpha. We reduce this to the special case of bounded X due to Wang and Wen in 2016 by using the inversion invariance of Assouad dimension. (c) 2021 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Subject: |
111 Mathematics
Assouad dimension Intermediate-value property Inversion |
| Peer reviewed: | Yes |
| Rights: | cc_by |
| Usage restriction: | openAccess |
| Self-archived version: | publishedVersion |
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Articles from TUHAT CRIS [46655]