On Most Generalized Topologies on a Non Empty Set

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2014 by IJMTT Journal
Volume-7 Number-1                          
Year of Publication : 2014
Authors : A.Gowri , Dr.S.Durai Raj


A.Gowri , Dr.S.Durai Raj. "On Most Generalized Topologies on a Non Empty Set", International Journal of Mathematical Trends and Technology (IJMTT). V7:19-26 March 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

The purpose of this paper is to introduce a notion of continuity called (G ,D)- continuity between two non empty sets X and Y, and its relationships with other functions are studied.


[1] 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.
[2] D.Andrijevic,Semi-pre-open sets.Mat.Vesnik 38(1986),24-32
[3] M.Anitha and P. Thangavelu, On pre-generalized pre-regular closed sets, Acta Ciencia Indica, 31 (4)(2005), 1035 -1040.
[4] P.Bhattacharyya and B.K. Lahiri, Semi-generalized closed sets in Topology, Ind. Jr. Math., 29(1987), 375-382.
[5] W. Dunham and N.Levine, Further results on generalized closed sets, Kyungpook Math. J.20 (1980), 169-175.
[6] Y. Gnanambal, On generalized preregular closed sets in topological spaces, Indian .J. Pure appl.Math. 28(3)(1997), 351-360.
[7] James Dugundji, Topology, Universal Book Stall, New Delhi, 1993.
[8] N.Levine, Semi-open sets and Semi- continuity in topological spaces, Amer. Mat.Monthly 70(1)(1963), 36-41. [9] N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19(2)(1970), 89-96.
[10] H.Maki, J.Umehara, T.Noiri, Every topological space is pre-T1/2, Mem.Fac. Sci. Kochi.Univ. (Math), 17(1996), 33-42.
[11] A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, OnPrecontinuous and Weak precontinuous mappings, Proc.Math.Phys.Soc.Egypt 53(1982), 47-53.
[12] A.S.Mashhour and I.A.Hasanein and S.N.El-Deeb,α-continuous and α-open mappings,Acta Math.Hungar.42(1983),213-218.
[13] O. Njastad, Some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
[14] N.Palaniappan and K.Chandrasekhara Rao, Regular generalized closed sets, Kyungpook Mathematical Journal, 33(2)(1993), 211-219.
[15] M. H. Stone, Applications of the theory of Boolean rings to the general topology, Trans. A.M.S. 41(1937), 375-481.

(G, D)-Continuity, G-interior, G-closure.