δω-Continuity and some Results on δω-Closure Operator

Manjeet Singh, Asha Gupta, Kushal Singh and Tareq Al-shami

Journal of Mathematics, 2022, vol. 2022, 1-8

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7767378

DOI: 10.1155/2022/7767378

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