International Journal of Nonlinear Analysis and Applications

Fibrewise Slightly Perfect Topological Spaces

Document Type : Research Paper

Authors

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

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

Abstract

The primary objective of this paper is to present a new concept of fibrewise topological spaces over B is said to be fibrewise slightly topological spaces over B. Also, we introduce the concepts of fibrewise slightly perfect topological spaces, filter base, contact point, slightly convergent, slightly directed toward a set, slightly adherent point, slightly rigid, fibrewise slightly weakly closed, H.set, fibrewise almost slightly perfect, slightly∗.continuous fibrewise slightly∗topological spaces respectively, slightly Te, locally QHC, In addition, we state and prove several propositions related to these concepts.  

Keywords

[1] A. Abo Khadra, S. S. Mahmoud, and Y. Y. Yousif, fibrewise near topological spaces, Journal of Computing, USA, 14 (2012) 1725-1736 .
[2] C. Kariofillis, On pairwise almost compactness, Ann. Soc. Sci Bruxelles (1986) 100-129 .
[3] I. M. James, General topology and homotopy theory, Springer-Verlag, New York, (1984).
[4] I. M. James, fibrewise topology, Cambridge University Press, London (1989).
[5] R. C. Jain and A. R. Singal, Slightly continuous mappings, Indian Math. Soc., 64 (1997) 195-203.
[6] G. Mohammed and Y. Y. Yousif, Fibrewise slightly topological spaces, (Submitted for published) (2020).
[7] M. Mukherjee, J. Nandi and S. Sen, On bitopological QHC spaces, Indian Jour. Pure Appl. Math. 27 (1996) 245-255.
[8] N. Bourbaki, General Topology, Part I, Addison Wesley, Reading, Mass, (1996).
[9] R. Englking, Outline of general topology, Amsterdam, (1989).
[10] S. Bose and D. Sinha, Almost open, almost closed, θ continuous and almost quasi- compact mappings in bitopological spaces, Bull. Cal.Math. Soc. 73 (1981) 345.
[11] Y. Y. Yousif, Some Results on Fiberewise Topological Spaces, Ibn Al Haitham Journal for Pure and Applied Science, University of Baghdad Collage of Education Ibn Al Haitham, 2 (2008) 118-132.
[12] Y. Yousif and L. Hussain, Fiberwise IJ-perfect bitopological spaces, Conf. Series: Journal of Physics. 1003, 012063 (2018) 1-12, doi: 10, 1088/1742-6596/1003/1/012063.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 1051-1059
  • Receive Date: 14 March 2021
  • Revise Date: 27 April 2021
  • Accept Date: 17 May 2021