İbtissam BUKHATWA, Sibel DEMİRALP

8485

On Some Generalized Open Sets in Ideal Bitopological Spaces

In this article, we introduce and study the concepts of \gammaij- I -sets, \gammaij - preI -open sets, and \gammaij -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,

PDF

___

  • 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.
Journal of New Theory-Cover
  • Yayın Aralığı: 4
  • Başlangıç: 2014
  • Yayıncı: Naim Çağman
Arşiv
Sayıdaki Diğer Makaleler

Raghavan ASOKAN, Ochanan NETHAJİ, Ilangovan RAJASEKARAN

Rayappan PRİNCY, Krishnaswamy MOHANA

Elif SARIKAYA, Melek GÖKBULUT, Gulhan GULER, Halis BOZKURT, İbrahim YİĞİTOĞLU, Arzu COŞKUN

Ilyas Razzag BABAYEV, Hafiz Shahhuseyn MUKHTAROV, Rafig Azizagha HUSEYNOV

Adel Mohammed Ali AL-QASHBARİ

Selçuk TOPAL

Ayşe ÇOBANKAYA

Rana Muhammad ZULQARNAIN, Muhammad SAEED, Bagh ALİ, Sohaib ABDAL, Muhammad SAQLAIN, Muhammad İrfan AHAMAD, Zeeshan ZAFAR

Rasul RASULİ

İbtissam BUKHATWA, Sibel DEMİRALP