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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P525

Roll of γδΩ-open sets in Digital Topology


Meenarani S.M, Poorani.K, Anbuchelvi.M
Abstract

This work is based on quasi-operation in a topological space. Quasi-operation has been extended to the class of Ω-open sets. The new class of γδΩ- open sets. The new class of γδΩ- open sets has been introduced by linking the set of all δ-open sets with quasi-operation on δ-open sets. Also two kinds of closures such as γ(δΩ)-closure and γδΩ-closure have been studied and derived their elementary properties. Moreover, γδ-regular and γδ-open quasi-operation have been investigated. Also γ(δΩ)-regular space has been defined and a few basic results on it have been derived.

Keywords
γδΩ-open set, γδΩ-closure, γδΩ-kernel, γδΩ-interior, γδΩ-closure, γδ-regular quasi-operation, γδ-open quasi-operation and γ(δΩ)-regular space.
References

[1] S.Kasahara, Operation compact spaces, Math. Japonica, 24 1, pp. 97-105, 1979.
[2] M.Lellis Thivagar, and M.Anbuchelvi, Note on Ω-closed sets in topological spaces, Mathematical Theory and Modeling, pp.50-58, 2012.
[3] S.M.Meenarani, K.Poorani, and M.Anbuchelvi, Operation on Ω-closed sets, Malaya Journal of Matematik, Vol. S. No. 1, pp.7-11, 2019.
[4] H.Ogata, Operation on topological spaces and associated topology, Math. Japonica, 36 1, pp. 175-184, 1991.
[5] M.H. Stone Applications of the theory of boolean rings to general topology , Trans. A. M. S., 41, pp.375-481, 1937.
[6] Velicko, N.V., H-closed topological spaces, Amer. Math. Soc. Transl. 2, 78, pp.103-118, 1968.

Citation :

Meenarani S.M, Poorani.K, Anbuchelvi.M, "Roll of γδΩ-open sets in Digital Topology," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 220-227, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P525

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