International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 98760, 7 pages
doi:10.1155/IJMMS/2006/98760

Mappings and decompositions of continuity on almost Lindelöf spaces

A. J. Fawakhreh1 and A. Kiliçman2

 1Department of Mathematics, Philadelphia University, P.O. Box 1, Amman 19392, Jordan
2Department of Mathematics, University Putra Malaysia, Selangor 43400, Serdang, Malaysia
Received 18 September 2005; Revised 4 January 2006; Accepted 12 March 2006

Abstract

A topological space X is said to be almost Lindelöf if for every open cover {Uα:α∈Δ} of X there exists a countable subset {αn:n∈ℕ}⊆Δ such that X=∪n∈ℕCl(Uαn). In this paper we study the effect of mappings and some decompositions of continuity on almost Lindelöf spaces. The main result is that a image of an almost Lindelöf space is almost Lindelöf.