Some Results on Pixley–Roy Hyperspaces
In this paper, we prove that if a space X has a point-countable cn-network, then the Pixley-Roy hyperspace PRX also has a point-countable cn-network. If X is a regular space with a point-countable ck-network, then so does the Pixley-Roy hyperspace PRX. Moreover, if X has a point-countable sp-network...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5878044 |
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| author | Ljubiša D. R. Kočinac Luong Quoc Tuyen Ong Van Tuyen |
| author_facet | Ljubiša D. R. Kočinac Luong Quoc Tuyen Ong Van Tuyen |
| author_sort | Ljubiša D. R. Kočinac |
| collection | DOAJ |
| description | In this paper, we prove that if a space X has a point-countable cn-network, then the Pixley-Roy hyperspace PRX also has a point-countable cn-network. If X is a regular space with a point-countable ck-network, then so does the Pixley-Roy hyperspace PRX. Moreover, if X has a point-countable sp-network (resp., strict Pytkeev network), then the Pixley–Roy hyperspace PR2X also has a point-countable sp-network (resp., strict Pytkeev network). On the other hand, we show that if the Pixley–Roy hyperspace PRX has a countable cn-network (resp., sp-network and strict Pytkeev network), then so does X. By these results, we obtain that if the Pixley–Roy hyperspace PRX is a cosmic space (resp., P0-space, strict P0-space, and stric P0-space), then so is X. Furthermore, the Pixley-Roy hyperspace PRnS2 is not a k-space for each n≥2. |
| format | Article |
| id | doaj-art-cf4e07948a784243b01fc423e834385f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cf4e07948a784243b01fc423e834385f2025-02-03T06:01:25ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5878044Some Results on Pixley–Roy HyperspacesLjubiša D. R. Kočinac0Luong Quoc Tuyen1Ong Van Tuyen2University of NišDepartment of MathematicsHoa Vang High SchoolIn this paper, we prove that if a space X has a point-countable cn-network, then the Pixley-Roy hyperspace PRX also has a point-countable cn-network. If X is a regular space with a point-countable ck-network, then so does the Pixley-Roy hyperspace PRX. Moreover, if X has a point-countable sp-network (resp., strict Pytkeev network), then the Pixley–Roy hyperspace PR2X also has a point-countable sp-network (resp., strict Pytkeev network). On the other hand, we show that if the Pixley–Roy hyperspace PRX has a countable cn-network (resp., sp-network and strict Pytkeev network), then so does X. By these results, we obtain that if the Pixley–Roy hyperspace PRX is a cosmic space (resp., P0-space, strict P0-space, and stric P0-space), then so is X. Furthermore, the Pixley-Roy hyperspace PRnS2 is not a k-space for each n≥2.http://dx.doi.org/10.1155/2022/5878044 |
| spellingShingle | Ljubiša D. R. Kočinac Luong Quoc Tuyen Ong Van Tuyen Some Results on Pixley–Roy Hyperspaces Journal of Mathematics |
| title | Some Results on Pixley–Roy Hyperspaces |
| title_full | Some Results on Pixley–Roy Hyperspaces |
| title_fullStr | Some Results on Pixley–Roy Hyperspaces |
| title_full_unstemmed | Some Results on Pixley–Roy Hyperspaces |
| title_short | Some Results on Pixley–Roy Hyperspaces |
| title_sort | some results on pixley roy hyperspaces |
| url | http://dx.doi.org/10.1155/2022/5878044 |
| work_keys_str_mv | AT ljubisadrkocinac someresultsonpixleyroyhyperspaces AT luongquoctuyen someresultsonpixleyroyhyperspaces AT ongvantuyen someresultsonpixleyroyhyperspaces |