On Some Types of Faint Continuity

A.A. El-Atik

Abstract

Using the concept of pre--open sets and semi--open sets, we introduce and investigate two forms of faint continuity which are called faint pre--continuity and faint semi--continuity. We obtain their characterizations, their basic properties and their relationships with other forms of functions between topological spaces. Also some results of Noiri-Popa, El-Atik and Nasef are improved. Finally, we discuss the product of faintly pre--continuous and faintly semi--continuous functions.