ON $N_{nc} \mathcal{DP^*}$-SETS AND DECOMPOSITION OF CONTINUITY IN $N_{nc}$-TOPOLOGICAL SPACES

A. Vadivel, M. Navuluri and P. Thangaraja

  DOI:  https://doi.org/10.37418/amsj.9.11.59

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The main goal of this paper is to study some new classes of sets and to obtain some new decompositions of continuity. For this aim, the notions of $N_{nc} \mathcal{DP}$ sets, $N_{nc} \mathcal{DP}\epsilon$ sets, $N_{nc} \mathcal{DP^*}$ sets, $N_{nc} \mathcal{DP}\epsilon^*$ sets, $N_{nc} e$ continuous functions, $N_{nc} \mathcal{DP^*}$ continuous functions and $N_{nc} \mathcal{DP}\epsilon^*$ continuous functions are introduced. Properties of $N_{nc} \mathcal{DP}$ sets, $N_{nc} \mathcal{DP}\epsilon$ sets, $N_{nc} \mathcal{DP^*}$ sets, $N_{nc} \mathcal{DP}\epsilon^*$ sets and the relationships between these sets and the related concepts are investigated. Finally, some new decompositions of continuity are obtained.

Keywords: $ N_{nc} \mathcal{DP} $-set, $ N_{nc} \mathcal{DP}\epsilon$-set, $ N_{nc} \mathcal{DP^*}$-set, $ N_{nc} \mathcal{DP}\epsilon^*$-set, $ N_{nc} e$ continuous function, decomposition