Year: 2022
Type: preprint
Abstract: We prove that for two connected sets $E,F\subset\mathbb{R}^2$ 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.
Source: arXiv (Cornell University)
Author: Wu, Yu-Feng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4285038647