We study sets of points at which \omega_1 sequences of real functions from a given class F converge. As F we consider continuous functions, first class of Baire, Borel measurable functions, functions with Baire property and Lebesgue measurable functions. Connections of those problem with additional set-theoretic axioms are discussed.

LaTeX 20.09 source file. Requires amsfonts and amssymb style files.

Last modified February 3, 2000.