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: University of Helsinki, Department of Mathematics and Statistics
Date: 2021-04-20
Number of pages: 2
Belongs to series: Topology and Its Applications
ISSN: 0166-8641
URI: http://hdl.handle.net/10138/329617
Abstract: We prove that if Xis a metric space of Assouad dimension s ∈(0, ∞), then for every α ∈[0, s]there is a countable subset ofXof Assouad dimensionα. We reduce this to the special case of boundedXdue to Wang and Wen in 2016 by using the inversion invariance of Assouad dimension.
Subject: 111 Mathematics
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