ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 26,46,54 Maslyuchenko, Volodymyr, Chernivtsi University, Ukraine Separately continuous mappings: Van Vleck spaces and inverse problems New results on the size of the set C(f) of joint continuity points of separately continuous mappings are presented. We say that Y is a Van Vleck space if the set of all x for which {x} × Y ⊆ C(f) is dense in X for every Baire space X, metrizable space Z and mapping f : X ×Y → Z from a class \overline{C}C. It is shown that mappings from a class \overline{K}C have the same property for hereditarely separable Van Vleck space too. This gives us a possibility to obtain new theorems on joint continuity of SCF of n variables which are closely related to Hahn’s, Feiock’s, Talagrand’s and Troallic’s results. Besides problems on the construction of SCF with a given set of discontinuity points, an oscillation or a diagonal are investigated. Part of these results is joint work with V. Mykhaylyuk, O. Sobchuk, V. Nesterenko and O. Maslyuchenko.