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math.CA2025
Fifty years of the Erdős similarity conjecture
Yeonwook Jung, Chun-Kit Lai, Yuveshen Mooroogen
Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickn…
math.CA2024
Topological Erdős similarity conjecture and strong measure zero sets
Yeonwook Jung, Chun-Kit Lai
We resolve the topological version of the Erdős Similarity conjecture introduced previously by Gallagher, Lai and Weber. We show that a set is topologically universal on ${\mathbb…
math.CA2023
Erdős similarity problem via bi-Lipschitz embedding
De-jun Feng, Chun-Kit Lai, Ying Xiong
The Erdős similarity conjecture asserted that an infinite set of real numbers cannot be affinely embedded into every measurable set of positive Lebesgue measure. The problem is sti…