A Generalized Form of G^*-Open Sets

Rajesh Kumar Tiwari¹ , J. K. Maitra² , Ravi Vishwakarma³

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.53-58, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.5358

Online published on Dec 31, 2018

Copyright © Rajesh Kumar Tiwari, J. K. Maitra, Ravi Vishwakarma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Generalization of sets in topological space is a very important concept in modern mathematics for structural oriented techniques. To enrich the structure and properties of generalized open sets, we define the notion of p^*-open sets by using topological space and generalized topological space both on the set X. The main aim of this paper is to define p^*-open sets and its generalized sets p^*-I-open sets, I_(p^* )-open sets and weakly I_(p^* )-open sets in a space (both topological space and generalized topological space) via ideal with illustrative examples. Also, we study the significant properties of newly defined open sets in the set X.

Key-Words / Index Term :
Generalized topology, ideal topological spaces, G-open sets, p^*-open sets, I_(p^* )-open sets

References :
Levin, N., Semi-open sets and Semi-continuity in topological spaces, Amer. Math. Monthly, 70, 36-41, 1963.
Dontchev, J., On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2, 1996.
Njasted, O., On some classes of nearly open sets, Pacific J. Math. Sci., 10(3), 393-396, 1965.
Abd El-Monsef, M. E., El-Deep, S.N., & Mahmoud, R.A., β-open set and β-continuous mapping. Bull. Fac. Sci. Assiut univ., 12, 77-90, 1983.
Csaszar, A., Generalized topology, generalized continuity. Acta Math. Hungar., 96, 351-357, 2002.
Csaszar, A., Generalized open sets in generalized topologies. Acta Math. Hungar, 106, 53-66, 2005.
Dontchev, J., On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2, 1996.
Roy B., Sen R., Generalized semi-open and pre-semi-open sets via ideals, Transactions of A. Razmadze Mathematical institute, 127, 95–100, 2015.
Kuratowski, K., Topology (Vol. 1), Academic Press, New York, 1966.
Vaidyanathaswamy, R., The localization theory in set-topology, Proc. Indian Acad. Sci. 20, 15–51, 1945.
Hatir E., T. Noiri, On semi-I-open set and semi-I-continuous functions, Acta Math. Hungar. 107, 345–353, 2005.
Mukherjee M. N., B. Roy, R. Sen, On extension of topological spaces in terms of ideals, Topology Appl. 154, 3167–3172, 2007.
Jankovic D., Hamlett T.R., New topologies from old via ideals, Amer. Math. Monthly 97 295–310, 1990.
Roy B., Sen R., On a type of decomposition of continuity, Afr. Math. 26, 153–158, 2015.