Abstract—The main aim of this paper is to introduce and investigate two new classes of irresolute functions called completely e*-irresolute functions and completely weakly e*- irresolute functions in topological spaces by using the concept of e*-open sets was introduced by Erdal Ekici [1], and obtain some characterizations and several interesting properties concerning such these functions. Furthermore the relationships between these functions and some other types of continuous functions are also given.

Index Terms—E*-Open Sets, e*-irresolute functions, completely e*-irresolute functions, completely weakly e*- irresolute functions.

The authors are with Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, China (e-mail: (alaa_mf1970@yahoo.com).

Cite: Alaa. M. F. AL. Jumaili and Xiao-Song Yang, "On Completely E*-Irresolute and Completely Weakly E*-Irresolute Functions in Topological Spaces via E*-open sets," International Journal of Applied Physics and Mathematics  vol. 2, no. 5, pp. 323-327, 2012.