International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2011-2021

On generalized ω-closed sets

Khalid Y. Al-Zoubi

Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, Jordan

Received 31 October 2004; Revised 3 July 2005

Copyright © 2005 Khalid Y. Al-Zoubi. 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.


The class of ω-closed subsets of a space (X,τ) was defined to introduce ω-closed functions. The aim of this paper is to introduce and study the class of gω-closed sets. This class of sets is finer than g-closed sets and ω-closed sets. We study the fundamental properties of this class of sets. In the space (X,τω), the concepts closed set, g-closed set, and gω-closed set coincide. Further, we introduce and study gω-continuous and gω-irresolute functions.