International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 35-40
Weak openness and almost openness
Department of Mathematics, Francis Marion College, Florence 29501, South Carolina, USA
Received 29 June 1983
Copyright © 1984 David 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.
Weak openness and almost openness for arbitrary functions between topological spaces are defined as duals to the weak continuity of Levine and the almost continuity of Husain respectively. Independence of these two openness conditions is noted and comparison is made between these and the almost openness of Singal and Singal. Some results dual to those known for weak continuity and almost continuity are obtained. Nearly almost openness is defined and used to obtain an improved link from weak continuity to almost continuity.