Another weak forms of faint continuity

A function f:X→Y is said to be faintly continuous [Kyungpook Math. J. 22 (1982) 7] if f−1(V) is open in X for every θ-open set V of Y. In this paper, we introduce and investigate two weaken forms of faint continuity which are called faint α-continuity and faint γ-continuity. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces also, some results in (A.A. El-Atik, A study of some types of mappings on topological spaces, M.Sc. Thesis, Tanta University, Egypt, 1997) are improved. We speculate that weak-faint continuity may be relevant to the physics of fractal and Cantorian spacetime.