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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 $D\backslash P$ is a $\psi_1$-uniformdomain, and $D$ is a uniform domain if and only if $D\backslash P$ also is auniform domain, whenever $P$ is a closed countable subset of $D$ satisfying aquasihyperbolic separation condition. This condition requires that thequasihyperbolic distance (w.r.t. $D$) between each pair of distinct points in$P$ has a lower bound greater than or equal to $\frac{1}{2}$.

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