Weak forms of faint continuity and faint openness in topology
by
G. B. Navalagi
Department of Mathematics, G.H. College, Haveri-581110, Karnataka, India.

In 1982, Long et al [Kyungpook Math. J. 22(1982), 7-14] have defined the notion of faint continuity, a function f: X --> Y is called faintly continuous if for each x in X and \theta-open set V containing f(x), there exists an open set U containing x such that f(U) subset V. Recently in 1989, Shozo Sakai [Kyungpook Math. J. 29(1), (1989), 41-56] has introduced the class of faintly open functions between topological spaces. A function f: X --> Y is called faintly open if f(U) is open for each \theta-open set U in X, that is: f: (X, T(\theta)) --> Y is open. In this paper, we introduce and study the weak forms of faint continuity and faint openness which are called faintly *-continuity, faint preopenness, faint semiopenness, faint \beta-openness respectively.

Date received: June 24, 2000