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, Serdang 43400, Malaysia

Received 18 September 2005; Revised 4 January 2006; Accepted 12 March 2006

Copyright © 2006 A. J. Fawakhreh and A. Kiliçman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.