The centennial of the separate versus joint continuity
by
Zbigniew Piotrowski
Youngstown State University

Exactly one hundred years ago R.Baire published his "Sur les fonctions des variables reelles" Ann.Mat. Pura Appl. 3 (1899), 1-122; a modern treatise on function theory where, among other things, it was shown that every separately continuous function f : R ×R --> R is of the first class (of Baire). Quarter century ago, I.Namioka [Pacific J.Math. (1974)] significantly improved H.Hahn's result showing that if both X and Y are "nice" topological spaces and M is metric then for every separately continuous function f : X ×Y --> M there is a dense G-delta subset A of X, such that the cartesian product of A and Y is contained in the set C(f) of points of (joint) continuity of f.

In my talk I will try to present and organize the highlights of the past 100 years of research in this field.

Date received: February 8, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-30.