On the topology generated by tgr-closed sets

A. EL-Mabhouh; H. Al-Faiuomy

doi:https://doi.org/10.14445/22315373/IJMTT-V24P503

International Journal of Mathematics Trends and Technology

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Volume 24 | Number 1 | Year 2015 | Article Id. IJMTT-V24P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V24P503

On the topology generated by tgr-closed sets

A. EL-Mabhouh, H. Al-Faiuomy

Abstract

Although the family of all tgr-closed sets in a topological space (X, τ ) (breifly tgrC(X, τ )) is not a topology on X, it can be considered as a subbase for some topology. In this paper we define the topology generated by tgr-closed sets(which is denoted by τtgr), and study some properties of spaces whose topologies are generated by the family of tgr-closed sets. We prove that τtgr ⊆ τ if and only if τ is tgr-locally indiscrete. Also we define the topology generated by t*gr-closed sets. We also prove that τtgr = τt*gr if (X, τ ) is locally indiscrete.

Keywords

τtgr , τt*gr , tgr-locally indiscrete.

References

[1] S.I.Mahmood,On Generalized Regular Continuous Functions In Topological Spaces, Ibn Al- Haitham Journal for Pure and applied Science , Vol.25 , No.3 (2012) 377-384 .
[2] T. Indira, and K. Rekha ,Applications of *b-open Sets and **b-open Sets in Topological Spaces,Annals of Pure and Applied Mathematics , Vol.1 , No.1 (2012) 44-56 .
[3] J.Dontchave, Contra Continuous Functions and Strongly S-closed Spaces, Internet .J.Math and Math.Sci , Vol.19 , No.2 (1996) 303-310.
[4] C.W.Baker, Contra open functions and Contra closed functions, Mathematics Today , Vol.XV , (1997) 19-24.
[5] C.Janaki and V.Jeyanthi, A New Class of Contra Continuous Functions in Topological Spaces, International Refereed Journal of Engineering and Science , Vol.2 , No.7 , (2013) 44-51.
[6] D. Andrijevic, On b-open sets, (1996) , 59-64 .
[7] K.Dlaska, N.Ergun and M.Ganster, On the topology generated by semi regular sets, Indian.J. pure appl. Math , Vol.25 , No.2 , (1994) 1163-1170.
[8] S. Willard, General topology, University of Alberta, Adisson-wislly puplish- ing company,( 1970).
[9] A. El-Mabhouh and H. Al-Faiuomy ,New Classes of Closed Sets tgr-Closed Sets and t*gr − ClosedSets,HIKARILtd, V ol.10, no.5, (2015)211 − 220.

Citation :

A. EL-Mabhouh, H. Al-Faiuomy, "On the topology generated by tgr-closed sets," International Journal of Mathematics Trends and Technology (IJMTT), vol. 24, no. 1, pp. 24-31, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V24P503