A note on the removability of totally disconnected sets for analytic functions - Pokrovskii, A. V. (Ukrains’kyi Matematychnyi Zhurnal, 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 GE and such that for any point z_0E the real or imaginary part of f(z) vanishes at z_0.