Some types of fibrewise fuzzy topological spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), Baghdad University, Baghdad, Iraq

2 Department of Mathematics, College of Education for Pure Science, Ibn AL-Haitham, University of Baghdad, Baghdad-Iraq.

Abstract

The aim of this paper is to introduce and study the notion type of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where $j=\{\delta, \theta, \alpha, p, s, b, \beta\}$.

Keywords

[1] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82 (1981) 14–32.
[2] A. S. Bin Shahna, On fuzzy strong semi-continuity and fuzzy precontinuity, Fuzzy Sets Syst. 44 (1991) 303–308.
[3] C. L. Chang, Fuzz topological spaces, J. Math. Anal. Appl. 24 (1968) 182–190.
[4] M. H. Ghanim, E. E. Kerre and A. S. Mashhour, Separation axioms, subspaces and sums in fuzzy topology, J. Math. Anal. Appl. 102 (1984) 189–202.
[5] I.M. Hanafy, Fuzzy γ-open sets and fuzzy γ-continuity, J. Fuzzy Math. 7(2) (1999) 419–430.
[6] B. Hutton, Products of fuzzy topological spaces, Top. Appl. 11 (1980) 59–67.
[7] I. M. James, Fibrewise Ttopology, Cambridge University Press, London, 1989.
[8] P. P. Ming and L. Y. Mong, Fuzzy topology I. neighborhood structure of a fuzzy point and Moor-Smith convergence, J. Math. Anal. Appl. 76 (1980) 571–599.
[9] M. N. Mukherjee and S. P. Sinha, On some near–fuzzy continuous function between fuzzy topological spaces, J. Math. Anal. Appl. 34 (1990) 245–254.
[10] C. V. Negoita and D. A. Ralescu, Application of Fuzzy Sets to Systems Analysis, Basel, Stuttgart, 1975.
[11] J. H. Park, B. Y. Lee and J. R. Choi, Fuzzy θ-connectedness, J. Fuzzy Set Syst. 59 (1993) 237–244.
[12] A.D. Ray and P. Chettr, On Fuzzy Nearly Compact Regular Open Topology, Adv. Fuzzy Math. 4(1) (2009) 59–68,.
[13] S. Saha, Fuzzy δ-continuous mappings, J. Math. Appl. 126 (1987) 130–142 .
[14] S. S. Thakur and S. Singh, On fuzzy semi-preopen sets and fuzzy semi-pre continuity, Fuzzy Sets Syst. 98(3) (1998) 383–391.[15] Y. Y. Yousif and L. A. Hussain, Fibrewise bitopological spaces, Int. J. Sci. Res. 6(2) (2017) 978–983.
[16] Y. Y. Yousif and L. A. Hussain, Fibrewise IJ-perfect bitopological spaces, Ibn Al-Aaitham 1st. International Scientific Conference, IOP Conf. Series: Journal of Physics: Conf. Series 1003 (2018) 012063 doi :10.1088/1742-6596/1003/1/012063, 13-14 December (2017) pp. 1-12.
[17] Y. Y.Yousif and L. A. Hussain, Fibrewise pairwise bi-topological spaces, 1st. Scientific International Conference, College of Science, Al-Nahrain University,[DOI. 10.22401/SIC.1.21], 21-22 November (2017) pp.157-165.
[18] Y. Y. Yousif and M. A. Hussain, Fibrewise Soft Ideal Topological Spaces, Ibn Al-Aaitham 1st. International Scientific Conference, IOP Conf. Series: Journal of Physics: Conf. Series 1003 (2018) 012050 doi :10.1088/1742-6596/1003/1/012050, 13-14 December 2017, pp. 1-12.
[19] Y. Y. Yousif and M. A. Hussain, Fibrewise soft near separation axioms, The 23th Science Conference of College of Education, Al-Mustansiriyah University, 26-27 April (2017), pp.400-414.
[20] Y. Y. Yousif and M. A. Hussain, Fibrewise soft topological spaces, Int. J. Sci. Res. 6(2) (2017)) 1010–1019.
[21] Y. Y. Yousif and B. Khalil, Feeble regular and feeble normal spaces in α-topological spaces using graph, Int. J. Nonlinear Anal. 12 (2021) 415–423.
[22] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338–353.
Volume 12, Issue 2
November 2021
Pages 751-756
  • Receive Date: 16 February 2021
  • Revise Date: 10 March 2021
  • Accept Date: 27 April 2021