On P3-Paracompact Spaces
Mashhour et al. [1] introduced the notions of P1-paracompactness and P2-paracompactness of topological spaces in terms of preopen sets. In this paper, we introduce and investigate a weaker form of paracompactness which is called P3-paracompact. We obtain various characterizations, properties, exampl...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/80697 |
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| _version_ | 1849467631457796096 |
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| author | Khalid Al-Zoubi Samer Al-Ghour |
| author_facet | Khalid Al-Zoubi Samer Al-Ghour |
| author_sort | Khalid Al-Zoubi |
| collection | DOAJ |
| description | Mashhour et al. [1] introduced the notions of P1-paracompactness and P2-paracompactness of topological spaces in terms of preopen sets. In this paper, we introduce and investigate a weaker form of paracompactness which is called P3-paracompact. We obtain various characterizations, properties, examples, and counterexamples concerning it and its relationships with other types of spaces. In particular, we show that if a space (X,T) is quasi-submaximal, then (X,T) is paracompact if it is P3-paracompact. |
| format | Article |
| id | doaj-art-e78e0d99fa584165abc9f540d61fe72e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e78e0d99fa584165abc9f540d61fe72e2025-08-20T03:26:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/8069780697On P3-Paracompact SpacesKhalid Al-Zoubi0Samer Al-Ghour1Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 21163, JordanDepartment of Mathematics and Statistics, Faculty of Science, Jordan University of Science and Technology, Irbid 22110, JordanMashhour et al. [1] introduced the notions of P1-paracompactness and P2-paracompactness of topological spaces in terms of preopen sets. In this paper, we introduce and investigate a weaker form of paracompactness which is called P3-paracompact. We obtain various characterizations, properties, examples, and counterexamples concerning it and its relationships with other types of spaces. In particular, we show that if a space (X,T) is quasi-submaximal, then (X,T) is paracompact if it is P3-paracompact.http://dx.doi.org/10.1155/2007/80697 |
| spellingShingle | Khalid Al-Zoubi Samer Al-Ghour On P3-Paracompact Spaces International Journal of Mathematics and Mathematical Sciences |
| title | On P3-Paracompact Spaces |
| title_full | On P3-Paracompact Spaces |
| title_fullStr | On P3-Paracompact Spaces |
| title_full_unstemmed | On P3-Paracompact Spaces |
| title_short | On P3-Paracompact Spaces |
| title_sort | on p3 paracompact spaces |
| url | http://dx.doi.org/10.1155/2007/80697 |
| work_keys_str_mv | AT khalidalzoubi onp3paracompactspaces AT sameralghour onp3paracompactspaces |