New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators
In this paper, we introduce new forms of continuity, namely, weakly θs-continuity, weakly θsω-continuity, almost θs-continuity, and almost θsω-continuity defined via closure operators. These concepts bridge the gap between classical and weak continuity and provide new insights into their relationshi...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/8411230 |
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| author | Kushal Singh Asha Gupta |
| author_facet | Kushal Singh Asha Gupta |
| author_sort | Kushal Singh |
| collection | DOAJ |
| description | In this paper, we introduce new forms of continuity, namely, weakly θs-continuity, weakly θsω-continuity, almost θs-continuity, and almost θsω-continuity defined via closure operators. These concepts bridge the gap between classical and weak continuity and provide new insights into their relationships. We establish necessary and sufficient conditions under which these forms align with existing notions such as semi-θs-continuity, θsω-continuity, weak continuity, and usual continuity, especially under specific constraints on the domain or codomain space. Our findings highlight both the common ground and the key differences between weakly and almost continuity concepts. To support and illustrate our findings, the study incorporates a wide range of examples and counterexamples, providing a comprehensive understanding of these concepts. |
| format | Article |
| id | doaj-art-5eb2600ec4134545a2134ec29f8739a2 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5eb2600ec4134545a2134ec29f8739a22025-08-20T02:36:59ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/8411230New Continuity Concepts With Usual, Semi, and Semi-ω-Closure OperatorsKushal Singh0Asha Gupta1Department of MathematicsDepartment of MathematicsIn this paper, we introduce new forms of continuity, namely, weakly θs-continuity, weakly θsω-continuity, almost θs-continuity, and almost θsω-continuity defined via closure operators. These concepts bridge the gap between classical and weak continuity and provide new insights into their relationships. We establish necessary and sufficient conditions under which these forms align with existing notions such as semi-θs-continuity, θsω-continuity, weak continuity, and usual continuity, especially under specific constraints on the domain or codomain space. Our findings highlight both the common ground and the key differences between weakly and almost continuity concepts. To support and illustrate our findings, the study incorporates a wide range of examples and counterexamples, providing a comprehensive understanding of these concepts.http://dx.doi.org/10.1155/jom/8411230 |
| spellingShingle | Kushal Singh Asha Gupta New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators Journal of Mathematics |
| title | New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators |
| title_full | New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators |
| title_fullStr | New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators |
| title_full_unstemmed | New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators |
| title_short | New Continuity Concepts With Usual, Semi, and Semi-ω-Closure Operators |
| title_sort | new continuity concepts with usual semi and semi ω closure operators |
| url | http://dx.doi.org/10.1155/jom/8411230 |
| work_keys_str_mv | AT kushalsingh newcontinuityconceptswithusualsemiandsemiōclosureoperators AT ashagupta newcontinuityconceptswithusualsemiandsemiōclosureoperators |