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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12277 |
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| _version_ | 1866912331635621888 |
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| author | Alrawajfeh, Talal Hdeib, Hasan Z. |
| author_facet | Alrawajfeh, Talal Hdeib, Hasan Z. |
| contents | 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 $X$ 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 Lindelöf, paracompact, and metacompact spaces that are related to the property D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On D-spaces and Covering Properties Alrawajfeh, Talal Hdeib, Hasan Z. General Topology 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 $X$ 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 Lindelöf, paracompact, and metacompact spaces that are related to the property D. |
| title | On D-spaces and Covering Properties |
| topic | General Topology |
| url | https://arxiv.org/abs/2504.12277 |