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δω‐Continuity and some Results on δω‐Closure Operator

Author

Listed:
  • Manjeet Singh
  • Asha Gupta
  • Kushal Singh

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, 2022. "δω‐Continuity and some Results on δω‐Closure Operator," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7767378
    DOI: 10.1155/2022/7767378
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    References listed on IDEAS

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    1. Ahmad Al-Omari & Mohd Salmi Md Noorani, 2007. "Contra- ω -Continuous and Almost Contra- ω -Continuous," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-13, October.
    2. Khalid Y. Al-Zoubi, 2005. "On generalized ω -closed sets," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-11, January.
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