On D-spaces and Covering Properties
Abstract
In this thesis, we introduce the subject of D-spaces and some of its most important open problems which are related to well known covering properties. We then introduce a new approach for studying D-spaces and covering properties in general. We start by defining a topology on the family of all principal ultrafilters of a set called the principal ultrafilter topology. We show that each open neighborhood assignment could be transformed uniquely to a special continuous map using the principal ultrafilter topology. We study some structures related to this special continuous map in the category Top, then we obtain a characterization of D-spaces via this map. Finally, we prove some results on Lindel\"of, paracompact, and metacompact spaces that are related to the property D.
Cite
@article{arxiv.2504.12277,
title = {On D-spaces and Covering Properties},
author = {Talal Alrawajfeh and Hasan Z. Hdeib},
journal= {arXiv preprint arXiv:2504.12277},
year = {2025}
}