International Journal of Nonlinear Analysis and Applications

On $B^{ic}$-open set and $B^{ic}$-continuous function in topological spaces

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Women, University of Tikrit, Tikrit, Iraq

Abstract

In this paper, we have introduced a new class of sets in topological space called $B^{ic}$-open set and we have introduced and study the properties of $B^{ic}$-continuous function and topological properties.

Keywords

[1] B.S. Abdullah and A.A. Mohammed, On standard concept using ii-open sets, Open Access J. 6 (2019).
[2] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, β-open sets and β-continuous mappings Bull. Fac. Sci. Assiut. Univ. 12 (1983) 77–90.
[3] D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38 (1986) 24–32.
[4] S.W. Askander, The Property of Extended and Non-Exteneded Topological for Semi-Open, α-Open and i-Open Sets with Application, M.Sc. Thesis, College of Education, University of Mosul, 2011.
[5] S.W. Askander and A.A. Mohammed, i-open sets in topological spaces, Al-Rafidain J. Comput. Sci. Math. 12 (2018) 13–23.
[6] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70 (1963) 36–41.
[7] A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deeb, On pre-continuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt. 53 (1982) 47–53.
[8] L.K. Matindih and E. Moyo, On M-assiymetric semi-open and M-asymmetric semicontinuous multifunctions in bitopological spaces, Adv. Pure Math. 11 (2021) 218–236.
[9] L. Matindih, E. Moyo, D. Manyika and T. Sinyangwe, Some results of upper and lower M-asymmetric irresolute multifunctions in bitopological spaces, Adv. Pure Math. 11 (2021) 611–627.
[10] A. Metin and O. Alkan, On soft β-open sets and soft β-continuous functions, Sci. World J. 2014 (2014) Article ID 843456.
[11] A.K. Mousa and A. Ghareeb, On soft β-open sets and soft β-continuous functions, Abst. Appl. Anal. 2015, Article ID 515939.
[12] A.A. Mohammed and B.S. Abdullah, II-open sets in topological spaces, Int. Math. Forum 14 (2019) 41–48.
[13] A.A. Mohammed and S.W. Askandar, On i-open sets, UAE Math. Day Conf. American Univ. Sharjah, April 14, 2012.
[14] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1995) 961–970.
[15] E. Ryszard, General Topology, Second Edition, Sigma Series in Pure Mathematics, Heldermann Verlag, Berlin, 1989.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 737-744
  • Receive Date: 01 August 2021
  • Revise Date: 01 July 2021
  • Accept Date: 27 September 2021