New Class of Closed Sets in Bitopological Spaces

S.V. Vani¹ , G. Priscilla Pacifica²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.409-413, Aug-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.409413

Online published on Aug 31, 2018

Copyright © S.V. Vani, G. Priscilla Pacifica . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

708 Views    216 Downloads    124 Downloads

Abstract :
The concept of bitopological space was first introduced by J.C.Kelly in 1963 (i.e) a non empty set X equipped with two arbitrary topologies τ_1 and τ_2.The concept of generalized closed sets plays a significant role in general topology and these are the research topics of many Topologists worldwide.In 1970 Norman Levine introduced the concept of generalization of closed sets in topological spaces and he defined the semi-open sets and semi-continuity in bitopological spaces. In this paper we introduce a new class of generalized closed sets namely (i,j) - g^(##) -closed sets in bitopological spaces (i.e)a subset A of a bitopological space (X,τ_1,τ_2 ) is called (i,j)-g^(##)-closed if τ_j-cl(A)⊆U,whenever A⊆U,U is τ_i-g^#-open in (X,τ_1 〖,τ〗_2 ) and some of the properties were discussed. The class of (i,j) - g^(##)-closed sets settled in between the class of (i,j) -g^*- closed sets and the class of (i,j)- gs- closed sets.Some of the basic properties of (i,j)-g^(##)- closed sets are investigated.

Key-Words / Index Term :
Topological spaces , Bitopological spaces, (i,j)- g^(##)-closed sets.

References :
[1] Arockiarani,studies on generalizations of generalized closed sets and maps in topological spaces,Ph.d.,Thesis,Bharathiar Univ,Coimbatore,1997.
[2] Bhattacharyia.P and Lahiri.B.K, semi generalized closed sets in Topology, Rend.circ, Math.Palermo, 19(2) (1970), 89-96.
[3] R.Devi, K.Balachandran and H.Maki, semi-generalized closed maps and generalized closed maps, Mem.Eac.Sci.Kochi Unvi.Ser.A.Math.,14(1993), 41-54.
[4] L.Elvina Mary,E.L.Mary Tency,A study on (i,j)-(Gs)^*-closed sets in bitopological spaces,IJOSER,vol 3 issue 1 january-2015.
[5] J.C.Kelley,Proc.London Math.Sci.,13(1963),71-89.
[6] Levine.N.Generalised closed sets in topology, Rend, circ, Math.palermo, (19)(2)(1970), 86-96.
[7] Mashhour.A.S.,AbdEl-deeb.S.N.,α-open mappings, Acta.Math.Hungar, 41 (1983),213-218
[8] S.Pauline Mary Helen.M, SindhuSurya.R, (i,j) strongly a^(**)-closed sets in Bitopological spaces,IJMTT(2014).
[9] M.K.R.S.Veerakumar, between closed sets and g-closed sets, Mem.Fac.Kochi Unvi.ser.A, Math., 17(1996), 33-42.