Weak openness and almost openness. (English) Zbl 0562.54020

Rose, David A.

Int. J. Math. Math. Sci. 7, 35-40 (1984).

Summary: 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.

MSC:

54C10

Special maps on topological spaces (open, closed, perfect, etc.)

Keywords:

weakly open maps; almost open maps; weak continuity; almost continuity