On Some Generalized Open Sets in Ideal Bitopological Spaces

Year 2020, Issue: 32, 1 - 10, 30.09.2020

İbtissam Bukhatwa Sibel Demiralp

Abstract

In this article, we introduce and study the concepts of \gamma_ij- I -sets, \gamma_ij - preI -open sets, and \gamma_ij -b-I -open sets by generalizing (i,j)-I-open, (i,j)-preI-open, and (i,j)-bI- open sets, respectively, in ideal bitopological spaces with an operation \gamma: \tau \rightarrow P(X). Further, we describe and study (\gamma, \delta)_ij-bI-continuous functions in ideal bitopological spaces through this paper                                                                                                                                                                                                                                                                                      .

Keywords

Ideal bitopological space, \gamma _{ij}-I- open sets, \gamma_{ij} - preI -open sets, gamma _{ij}-bI-open sets, \gamma _{ij}-I-continuous functions

References

• J. C. Kelly, Bitopological Spaces, Proceedings of the London Mathematical Society 3(1) (1963) 71-89.
• K. Kuratowski, Topology Vols 1 and 2, Academic Press (1966).
• S. Kasahara, Operation-Compact Spaces, Mathematica Japonica 24(1) (1979) 97-105.
• F. H. Khedr, Operation on Bitopologies, Delta Journal Of Science 8(1) (1984) 309-320.
• F. H. Khedr, K. H. Abdelhakiem, Operations on Bitopological Spaces, Fasciculi Mathematici 45 (2010) 47-57.
• D. Andrijevic, On b-open Sets, Matematicki Vesnik 205 (1996) 59-64.
• T. Al-Hawary, A. Al-Omari, b-open and b􀀀continuity in Bitopological Spaces, Al-Manarah 13(3) (2007) 89-101.
• A. C. Guler, G. Aslim, bI-open Sets and Decomposition of Continuity via Idealization, Proceedings of Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan 22 (2005) 27-32.
• E. Ekici, On Pre-I-open sets, Semi-I-open sets and b-I-open sets in Ideal Topological Spaces, Acta Universitatis Apulensis 30 (2012) 293-303.
• N. Rajesh, M. Caldas, S. Jafari, Preopen Sets in Ideal Bitopological Spaces, Boletim da Sociedade Paranaense de Matematica 29(2) (2011) 61-68.
• H. Z. Ibrahim, On Pre-I-Open Sets In Ideal Topological Spaces, arxiv preprint arxiv: 1501.02494. 2015 Jan 11.
• S. D. Jyoti, bI-open Sets in Ideal Bitopological Space, International Journal of Pure and Applied Mathematics 105(1) (2015) 7-18.
• S. Hussain, On Generalized Open Sets, Hacettepe Journal of Mathematics and Statistics 47(6) (2018) 1438-1446.
• I. Bukhatwa, S. Demiralp, On Generalized -Open Sets in Ideal Bitopological Space, European Journal of Pure and Applied Mathematics 13(2) (2020) 269-279.
• M. Ilkhan, M. Akyigit, E. E. Kara, On New Types of Sets via 􀀀open Sets in Bitopological Spaces, Communications Series A1 Mathematics & Statistics 67(1) (2017) 225-234.
• M. Kar, S. S. Thakur, S. S. Rana, J. K. Maitra, I-Continuous Functions in Ideal Bitopological Spaces, American Journal of Engineering Research 3(3) (2014) 51-55.
• M. Akdağ, On bI-open Sets and bI-continuous Functions, International Journal of Mathematics and Mathematical Sciences Article ID 75721 (2007) 13 pages.
• M. Caldas, S. Jafari, N. Rajesh, Some Fundamental Properties of Beta-open Sets in Ideal Bitopo- logical Spaces, European Journal of Pure and Applied Mathematics 6(2) (2013) 247-255.
• B. C. Tripathy, D. J. Sarma, Generalized b-closed Sets in Bitopological Spaces, Proyecciones (Antofagasta) 33(3) (2014) 315-324.
• J. K. Maitra, H. K. Tripathi, Local Function in Generalized Ideal Topological Spaces, VISLESANA 11(1) (2014) 191-195.
• H. Ogata, Operations on Topological Spaces and Associated Topology, Mathematica Japonica 36 (1991) 175-184.
• G. Şenel, N. Cağman, Soft Closed Sets on Soft Bitopological Space, Journal of New Results in Science 3(5) (2014) 57-66.
• G. Şenel, On Bitopological Spaces, Master's Thesis, Ege University (2009) Izmir, Turkey.
• R. Vaidyanathaswamy, The Localisation Theory in Set Topology, Proceedings of the Academic of Sciences, 20 (1945) 51-61.