On removability properties of $psi$-uniform domains in Banach spaces


Abstract in English

Suppose that $E$ denotes a real Banach space with the 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 $Dbackslash P$ is a $psi_1$-uniform domain, and $D$ is a uniform domain if and only if $Dbackslash P$ also is a uniform domain, whenever $P$ is a closed countable subset of $D$ satisfying a quasihyperbolic separation condition. This condition requires that the quasihyperbolic distance (w.r.t. $D$) between each pair of distinct points in $P$ has a lower bound greater than or equal to $frac{1}{2}$.

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