A Study On S-paracompact Spaces And α-expandable Spaces

In 2006, Al-Zoubi [1] introduced the definition of S-paracompact spaces, proved that every paracompact space is S-paracompact and studied properties on S-paracompact spaces. In our paper, we continue to study the properties on S-paracompact spaces. More precisely,In Chapter 1, we introduce necessary symbols and preliminaries which are used in this paper and summary the main results of this paper.In Chapter 2, first, we construct a Hausdorff S-paracompact space which is not a paracompact space. Next, we point out that the sufficiency of Theorem 2.14 in [1] is not valid by giving an example. Finally, we introduce a class of S-expandable spaces and show that every S-paracompact space is S-expandable.In Chapter 3, we introduce the definition ofα-expandable spaces, show that everyα-paracompact space isα-expandable and study the properties ofα-expandable spaces.