3 papers
math.CA2025
Interior of distance trees over thin Cantor sets
Yeonwook Jung, Krystal Taylor
It is known that if a compact set in has Hausdorff dimension greater than , then its -chain distance set $$Î^n(E) = \left\{\left(\left|x^1-x^2\right…
math.CA2025
Topological ErdÅs similarity conjecture and strong measure zero sets
Yeonwook Jung, Chun-Kit Lai
We resolve the topological version of the ErdÅs Similarity conjecture introduced previously by Gallagher, Lai and Weber. We show that a set is topologically universal on ${\mathbb…
math.CA2025
Fifty years of the ErdÅs similarity conjecture
Yeonwook Jung, Chun-Kit Lai, Yuveshen Mooroogen
ErdÅs similarity conjecture was proposed by P. ErdÅs in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thic…