International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 311-318

Weak continuity and almost continuity

D. A. Rose

Department of Mathematics, Francis Marion College, Florence 29501, South Carolina, USA

Received 28 March 1983

Copyright © 1984 D. A. Rose. 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.


Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended.