Tišer, J.; Zajíček, L. Typical measurable function in the topology of close approximation. (English) Zbl 0733.28001 Acta Math. Univ. Comen., New Ser. 60, No. 1, 23-29 (1991). Author’ abstract: It is shown that the typical Lebesgue or Baire measurable function with respect to the topology of close approximation has the range of second category and that there are nonempty open sets of the space of measurable functions where the typical function has \(G_{\delta}\) dense range and the preimage of every point of the range contains a perfect set. Reviewer: Z.Grande (Bydgoszcz) MSC: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 26A99 Functions of one variable 54C30 Real-valued functions in general topology 54C35 Function spaces in general topology Keywords:measurable function; topology of close approximation; typical function PDFBibTeX XMLCite \textit{J. Tišer} and \textit{L. Zajíček}, Acta Math. Univ. Comen., New Ser. 60, No. 1, 23--29 (1991; Zbl 0733.28001) Full Text: EuDML EMIS