δω-Continuity and some Results on δω-Closure Operator
Al-Jarrah et al. defined a new topological operator, namely, δω-closure operator, and proved that it lies between the δ-closure operator and the usual closure operator. Al-Ghour et al. defined θω-closure operator and discussed its properties. In this paper, it is proved that the δω-closure operator...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7767378 |
| _version_ | 1798031286302932992 |
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| author | Manjeet Singh Asha Gupta Kushal Singh |
| author_facet | Manjeet Singh Asha Gupta Kushal Singh |
| author_sort | Manjeet Singh |
| collection | DOAJ |
| description | Al-Jarrah et al. defined a new topological operator, namely, δω-closure operator, and proved that it lies between the δ-closure operator and the usual closure operator. Al-Ghour et al. defined θω-closure operator and discussed its properties. In this paper, it is proved that the δω-closure operator lies between the θω-closure operator and the usual closure operator. Also, sufficient conditions are given for the equivalence between the δω-closure operator and the θω-closure operator. Moreover, we define three new types of continuity, namely, δω-continuity, ω-δ-continuity, and almost δω-continuity, and discuss their properties. It is proved that the concepts of usual continuity and δω-continuity are independent of each other. In addition, the relationships between different types of continuity have been investigated. Further, some examples and counter examples are given. |
| first_indexed | 2024-04-11T19:53:56Z |
| format | Article |
| id | doaj.art-94dee7c8113c4cbfad9dc2f950e80d94 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-11T19:53:56Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-94dee7c8113c4cbfad9dc2f950e80d942022-12-22T04:06:13ZengHindawi LimitedJournal of Mathematics2314-47852022-01-01202210.1155/2022/7767378δω-Continuity and some Results on δω-Closure OperatorManjeet Singh0Asha Gupta1Kushal Singh2Department of Applied SciencesDepartment of Applied SciencesDepartment of Applied SciencesAl-Jarrah et al. defined a new topological operator, namely, δω-closure operator, and proved that it lies between the δ-closure operator and the usual closure operator. Al-Ghour et al. defined θω-closure operator and discussed its properties. In this paper, it is proved that the δω-closure operator lies between the θω-closure operator and the usual closure operator. Also, sufficient conditions are given for the equivalence between the δω-closure operator and the θω-closure operator. Moreover, we define three new types of continuity, namely, δω-continuity, ω-δ-continuity, and almost δω-continuity, and discuss their properties. It is proved that the concepts of usual continuity and δω-continuity are independent of each other. In addition, the relationships between different types of continuity have been investigated. Further, some examples and counter examples are given.http://dx.doi.org/10.1155/2022/7767378 |
| spellingShingle | Manjeet Singh Asha Gupta Kushal Singh δω-Continuity and some Results on δω-Closure Operator Journal of Mathematics |
| title | δω-Continuity and some Results on δω-Closure Operator |
| title_full | δω-Continuity and some Results on δω-Closure Operator |
| title_fullStr | δω-Continuity and some Results on δω-Closure Operator |
| title_full_unstemmed | δω-Continuity and some Results on δω-Closure Operator |
| title_short | δω-Continuity and some Results on δω-Closure Operator |
| title_sort | δω continuity and some results on δω closure operator |
| url | http://dx.doi.org/10.1155/2022/7767378 |
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