巴拿赫空间中$ψ$ -一致域的可去性
On removability properties of $ψ$-uniform domains in Banach spaces
摘要：
设$E$表示维数至少为2的实巴拿赫空间。本文的主要目的是证明$E$中的整环$D$是$ψ$ -一致整环当且仅当$D\backslash P$是$ψ_1$ -一致整环，并且$D$是一致整环当且仅当$D\backslash P$也是一致整环，只要$P$是$D$的一个闭可数子集满足一个拟双曲分离条件.该条件要求准双曲距离（w.r.t. $P$中每对不同点之间的距离（$D$）的下限大于或等于$\frac{1}{2}$。
英文摘要：
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 $ψ$-uniform domain if and only if $D\backslash P$ is a $ψ_1$-uniform domain, and $D$ is a uniform domain if and only if $D\backslash P$ also is a uniform domain, whenever $P$ is a 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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