Girnyk, M. A. Logarithms of moduli of entire functions are nowhere dense in the space of plurisubharmonic functions. (Russian, English) Zbl 1199.32010 Ukr. Mat. Zh. 60, No. 12, 1602-1609 (2008); translation in Ukr. Math. J. 60, No. 12, 1878-1888 (2008). Summary: We prove that the set of logarithms of moduli of entire functions of several complex variables is nowhere dense in the space of plurisubharmonic functions equipped with a topology that is a generalization of the topology of uniform convergence on compact sets. This topology is generated by a metric in which plurisubharmonic functions form a complete metric space. Thus, the logarithms of moduli of entire functions form a set of the first Baire category. MathOverflow Questions: Topology on the set of analytic functions MSC: 32A15 Entire functions of several complex variables 32U05 Plurisubharmonic functions and generalizations Keywords:entire function; plurisubharmonic function; complete metric space; first Baire category PDFBibTeX XMLCite \textit{M. A. Girnyk}, Ukr. Mat. Zh. 60, No. 12, 1602--1609 (2008; Zbl 1199.32010); translation in Ukr. Math. J. 60, No. 12, 1878--1888 (2008) Full Text: DOI