International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1988 / Article

Open Access

Volume 11 |Article ID 158729 | https://doi.org/10.1155/S0161171288000808

J. P. Lee, Z. Piotrowski, "Another note on Kempisty's generalized continuity", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 158729, 7 pages, 1988. https://doi.org/10.1155/S0161171288000808

Another note on Kempisty's generalized continuity

Received23 Sep 1987
Revised11 Nov 1987

Abstract

Under a fairly mild completeness condition on spaces Y and Z we show that every x-continuous function f:X×Y×ZM 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.

Copyright © 1988 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.


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