Δω-Continuity and some Results on δω-Closure Operator. (6th October 2022) - Singh, Manjeet; Gupta, Asha; Singh, Kushal
Abstract : Al-Jarrah et al. defined a new topological operator, namely, δ ω -closure operator, and proved that it lies between the δ -closure operator and the usual closure operator. Al-Ghour et al. defined θ ω -closure operator and discussed its properties. In this paper, it is proved that the δ ω -closure operator lies between the θ ω -closure operator and the usual closure operator. Also, sufficient conditions are given for the equivalence between the δ ω -closure operator and the θ ω -closure operator. Moreover, we define three new types of continuity, namely, δ ω -continuity, ω -δ -continuity, and almost δ ω -continuity, and discuss their properties. It is proved that the concepts of usual continuity and δ ω -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.