On Removability Properties of $$\psi $$ ψ -Uniform Domains in Banach Spaces

Abstract

Suppose that E is a real Banach space with dimension at least 2. The main aim of this paper is to show that a domain D in E is a \(\psi \)-uniform domain if and only if \(D\backslash P\) is a \(\psi _1\)-uniform domain, and D is a uniform domain if and only if \(D\backslash P\) also is a uniform domain, whenever P is a countable subset of D satisfying a quasihyperbolic separation condition. This condition requires that the quasihyperbolic distance with respect to D between each pair of distinct points in P has a lower bound greater than or equal to \(\frac{1}{2}\).