International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 54, Pages 3469-3477

Separately continuous functions: approximations, extensions, and restrictions

Zbigniew Piotrowski1 and Robert W. Vallin2

1Department of Mathematics and Statistics, Youngstown State University, Youngstown 44555, OH, USA
2Department of Mathematics, Slippery Rock University of Pennsylvania, Slippery Rock 16057, PA, USA

Received 23 August 2002

Copyright © 2003 Zbigniew Piotrowski and Robert W. Vallin. 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.


A function f(x,y) is separately continuous if at any point the restricted functions fx(y) and fy(x) are continuous as functions of one variable. In this paper, we use several results which have been obtained for other generalized continuities and apply them to functions which are separately continuous.