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δω-Continuity and some Results on δω-Closure Operator

Author

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  • Manjeet Singh
  • Asha Gupta
  • Kushal Singh
  • Tareq Al-shami

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.

Suggested Citation

  • Manjeet Singh & Asha Gupta & Kushal Singh & Tareq Al-shami, 2022. "δω-Continuity and some Results on δω-Closure Operator," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, October.
    • Handle: RePEc:hin:jjmath:7767378
    DOI: 10.1155/2022/7767378
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