Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces
In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regar...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/1/78 |
| _version_ | 1797446135041753088 |
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| author | Samer Al Ghour |
| author_facet | Samer Al Ghour |
| author_sort | Samer Al Ghour |
| collection | DOAJ |
| description | In this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft compactness, soft Lindelofness, soft connectedness, soft regularity, soft normality, soft almost regularity, soft mild normality, soft almost compactness, soft almost Lindelofness, soft near compactness, soft near Lindelofness, soft paracompactness, soft near paracompactness, soft almost paracompactness, and soft metacompactness are obtained. In addition to these, the study deals with the correlation between our new concepts in soft topology and their corresponding concepts in general topology; as a result, we show that soft complete continuity (resp. soft strong continuity) in soft topology is an extension of complete continuity (resp. strong continuity) in soft topology. |
| first_indexed | 2024-03-09T13:35:52Z |
| format | Article |
| id | doaj.art-36ad5701d7ab4f4ea0559ab5adc95aa6 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:35:52Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-36ad5701d7ab4f4ea0559ab5adc95aa62023-11-30T21:12:00ZengMDPI AGAxioms2075-16802023-01-011217810.3390/axioms12010078Soft Complete Continuity and Soft Strong Continuity in Soft Topological SpacesSamer Al Ghour0Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, JordanIn this paper, we introduce soft complete continuity as a strong form of soft continuity and we introduce soft strong continuity as a strong form of soft complete continuity. Several characterizations, compositions, and restriction theorems are obtained. Moreover, several preservation theorems regarding soft compactness, soft Lindelofness, soft connectedness, soft regularity, soft normality, soft almost regularity, soft mild normality, soft almost compactness, soft almost Lindelofness, soft near compactness, soft near Lindelofness, soft paracompactness, soft near paracompactness, soft almost paracompactness, and soft metacompactness are obtained. In addition to these, the study deals with the correlation between our new concepts in soft topology and their corresponding concepts in general topology; as a result, we show that soft complete continuity (resp. soft strong continuity) in soft topology is an extension of complete continuity (resp. strong continuity) in soft topology.https://www.mdpi.com/2075-1680/12/1/78completely continuous functionstrongly continuous functionsoft weakly continuous functionssoft nearly compactsoft nearly paracompact |
| spellingShingle | Samer Al Ghour Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces Axioms completely continuous function strongly continuous function soft weakly continuous functions soft nearly compact soft nearly paracompact |
| title | Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces |
| title_full | Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces |
| title_fullStr | Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces |
| title_full_unstemmed | Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces |
| title_short | Soft Complete Continuity and Soft Strong Continuity in Soft Topological Spaces |
| title_sort | soft complete continuity and soft strong continuity in soft topological spaces |
| topic | completely continuous function strongly continuous function soft weakly continuous functions soft nearly compact soft nearly paracompact |
| url | https://www.mdpi.com/2075-1680/12/1/78 |
| work_keys_str_mv | AT sameralghour softcompletecontinuityandsoftstrongcontinuityinsofttopologicalspaces |