Intermediate-value property for Assouad dimension by its inversion invariance

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http://hdl.handle.net/10138/329617

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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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