On Removability Properties of psi-Uniform Domains in Banach Spaces

摘要

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 -uniform domain if and only if is a -uniform domain, and D is a uniform domain if and only if 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 1/2.