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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 3, Pages 495-500
http://dx.doi.org/10.1155/S0161171296000695

On the theorems of Y. Mibu and G. Debs on separate continuity

Department of Mathematics, Youngstown State University, Youngstown, OH 44555, USA

Received 25 May 1994; Revised 1 November 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using a game-theoretic characterization of Baire spaces, conditions upon the domain and the range are given to ensure a “fat” set C(f) of points of continuity in the sets of type X×{y}, yY for certain almost separately continuous functions f:X×YZ. These results (especially Theorem B) generalize Mibu's. First Theorem, previous theorems of the author, answers one of his problems as well as they are closely related to some other results of Debs [1] and Mibu [2].