International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 657-663
doi:10.1155/S0161171288000808
Another note on Kempisty's generalized continuity
1Department of Mathematics, State University of New York, College at Old Westbury, Old Westbury 11568, NY, USA
2Department of Mathematical & Computer Sciences, Youngstown State University, Youngstown 44555, OH, USA
Received 23 September 1987; Revised 11 November 1987
Copyright © 1988 J. P. Lee and Z. Piotrowski. 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
Under a fairly mild completeness condition on spaces Y and Z we show that every x-continuous function f:X×Y×Z→M has a “substantial” set C(f) of points of continuity. Some odds and ends concerning a related earlier result shown by the authors are presented. Further, a generalization of S. Kempisty's ideas of generalized continuity on products of finitely many spaces is offered. As a corollary from the above results, a partial answer to M. Talagrand's problem is provided.