Interiors of continuous images of the middle-third Cantor set

2018/09/06 by Jiang, Kan, Xi, Lifeng
#Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.01880

Abstract

Let C be the middle-third Cantor set, and f a continuous function defined on an open set U⊂ ℝ². Denote the image f_U(C,C)=\f(x,y):(x,y)∈ (C× C)∩ U\. If ∂ _xf, ∂ _yf are continuous on U, and there is a point (x₀,y₀)∈ (C× C)∩ U such that \beginequation* 1

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