WEAK TANGENTS ON CLOSED POPCORN GRAPHS

Haipeng Chen () and Lixuan Zheng
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Haipeng Chen: College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, P. R. China
Lixuan Zheng: Department of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-9

Abstract: Given 0 < t < ∞, we study the Assouad dimension and weak tangents of closed t-popcorn graphs. For all 0 < t < 2, we prove that [0, 1]2 is a weak tangent of the closed t-popcorn graphs by using some arguments on prime numbers. For all 2 ≤ t < ∞, we first show that the Assouad dimension of the closed t-popcorn graphs is 1, and then prove that [0, 1] ×{0} is a weak tangent of them. We also discuss some specific weak tangents of closed t-popcorn graphs when t = 2 and 2 < t < ∞.

Keywords: Weak Tangents; Popcorn Functions; Popcorn Graphs; Assouad Dimension (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500731

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