On the Removability Property of φ -Natural Domains in Real Banach Spaces

Abstract

In this paper, we investigate the removability of $\phi$ -natural domains in Banach spaces. Let $E$ be a real Banach space with dimension at least 2, $G$ a domain in $E$ , and let be a countable subset of $G$ which satisfies a quasi hyperbolic separation condition. Then, $G$ is $\phi$ -natural if and only if $G$ is $\psi$ -natural, quantitatively.