On Assouad dimension of products

Fengji Peng, Wen Wang and Shengyou Wen

Chaos, Solitons & Fractals, 2017, vol. 104, issue C, 192-197

Abstract: We prove that, given 0 ≤ β ≤ α and α≤λ≤β+α, there exist compact subsets X, Y of the Euclidean space R⌈α⌉ such that dimAX=α,dimAY=β and dimA(X×Y)=λ, where ⌈α⌉ is the smallest integer ≥ α and dimA denotes Assouad dimension. In the proof an Assouad dimension formula for uniform Cantor sets is established.

Keywords: Assouad dimension; Uniform Cantor set; Product set (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:104:y:2017:i:c:p:192-197

DOI: 10.1016/j.chaos.2017.08.004

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