On arithmetic sums of connected sets in ℝ²

2022/07/08 by Yufeng Wu, Wu, Yu-Feng
Mathematics · #54D30 (Secondary) #54F15 (Primary) 54D05 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2207.03778

openalex publication_date 2022/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for two connected sets E,F⊂ℝ² with cardinalities greater than 1, if one of E and F is compact and not a line segment, then the arithmetic sum E+F has non-empty interior. This improves a recent result of Banakh, Jabłońska and Jabłoński [4,Theorem 4] in dimension two by relaxing their assumption that E and F are both compact.

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