Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2011, Article ID 270704, 9 pages doi:10.1155/2011/270704 Research Article On Quasi-ω-Confluent Mappings Abdo Qahis and Mohd. Salmi Md. Noorani School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia Correspondence should be addressed to Abdo Qahis, cahis82@gmail.com Received 4 March 2011; Accepted 28 April 2011 Academic Editor: Christian Corda Copyright q 2011 A. Qahis and Mohd. S. Md. Noorani. 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. We introduce a new class of mappings called quasi-ω-confluent maps, and we study the relation between these mappings, and some other forms of confluent maps. Moreover, we prove several results about some operations on quasi-ω-confluent mappings such as: composition, factorization, pullbacks, and products. 1. Introduction A generalization of the notion of the classical open sets which has received much attention lately is the so-called ω-open sets. These sets are characterized as follows 1: a subset W of a topological space X, τ  is an ω-open set if and only if for each x ∈ W, there exists U ∈ τ such that x ∈ U and U − W is countable. One can then show that the family of all ω-open subsets of a space X, τ , denoted by τ w , forms a topology on X finer than τ . Using this notion of ω-open sets, one can then define notions such as ω-compact and ω-connected sets whose definitions follow closely the definitions of the related classical notions. For example, a space X is called ω-connected provided that X is not the union of two disjoint nonempty ω-open sets. And X is said to be ω-compact if every ω-open cover of X has a finite subcover. For more information regarding these notions and some recent related results, see 2–4. Recall that a subset K of a space X is said to be a continuum if K is connected and compact. Using this idea of a continuum, Charatonik introduced and studied the idea of a confluent mapping between topological spaces 5 as follow: A mapping f : X → Y is said to be confluent provided that for each continuum K of Y and for each component C of f −1 K, we have f C K. In 6, motivated by Charatonik’s work, we have introduced the notion of ω-confluent mappings and studied its basic properties. In particular, we say a space X is an ω-continuum