A note on the removability of totally disconnected sets for analytic functions - Pokrovskii, A. V.; Покровський, А.В. (Institute of Mathematics, NAS of Ukraine, 2020)
UDC 517.537.38 We prove that each totally disconnected closed subset $E$ of a domain $G$ in the complex plane is removable for analytic functions $f(z)$ defined in $G\setminus E$ and such that for any point $z_0\in E$ the real or imaginary part of $f(z)$ vanishes at $z_0$.