(sp)* Closed Sets in Topological Spaces

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2014 by IJMTT Journal
Volume-7 Number-1                          
Year of Publication : 2014
Authors : L. Elvina Mary , R.Chitra


L. Elvina Mary , R.Chitra. "(sp)* Closed Sets in Topological Spaces", International Journal of Mathematical Trends and Technology (IJMTT). V7:68-82 March 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

In this paper we introduce a new class of sets namely, (sp)*-closed sets and properties of this set are investigated. We introduce (sp)*-continuous maps and (sp)*-irresolute maps.


[1] D. Andrijevic , Semi-preopen sets, Mat. Vesnik, 38(1) (1986), 24-32.
[2] I. Arokiarani, K.Balachandran and J. Dontchev, Some characterizations of gp-irresolute and gp-continuous maps between topological spaces, Mem. Fac. Sci. Kochi. Univ. Ser.A. Math., 20(1999), 93-104.
[3] S.P. Arya and T. Nour, Characterizations of s-normal spaces, Indian J. Pure. Appl. Math., 21(8)(1990), 717-719.
[4] K. Balachandran, P. Sundaram and H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Kochi Univ. Ser. A, Math., 12(1991), 5-13.
[5] P. Bhattacharya and B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3) (1987), 375-382.
[6] R. Devi, H. Maki and K. Balachandran, Semi-generalized homeomorphisms and generalized semi-homeomorphism in topological spaces, Indian J. Pure. Appl. Math., 26(3) (1995), 271-284.
[7] J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci. Kochi Ser.A, Math.,16(1995), 35-48.
[8]Y. Gnanambal, On generalized preregular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28(3)(1997), 351-360.
[9] N. Levine, Generalized closed sets topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.
[10] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
[11] H. Maki.H, R. Devi and K. Balachandran, Associated topologies of generalized -closed sets and -generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A, Math.,15(1994),51-63.
[12] H. Maki, R. Devi and K. Balachandran, Generalized -closed sets in topology, Bull. Fukuoka Univ. Ed. Part III, 42(1993), 13-21.
[13] H. Maki, J. Umehara and T. Noiri, Every topological spaces is pre- , Mem. Fac. Sci. Kochi. Univ. Ser.A, Math., 17(1996), 33-42.
[14] A.S. Mashhour, M.E. Abd. E1-Monsef and S.N.E1-Deep, On pre-continuous and weak pre-continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53(1982), 47-53.
[15] Nagaveni, studies on generalization of homeomorphisms in topological spaces, Ph. D thesis, Bharathiar university, Coimbatore, 1999.
[16] O. Njastad, On Some classes of nearly open sets, Pacific J. Math.,15(1965),961-970.
[17] M.K.R.S. Veerakumar, -closed sets and GIC-functions, Indian J. Math., 43 (2) (2001) 231-247.
[18] Veronica Vijayan, F. Priya, *-closed sets in topological spaces, IJCA, Issue 3, Volume 4 (July-Aug 2013), ISSN:2250-1797, 49-60.

(sp)*-closed sets, (sp)*-continuous and (sp)*-irresolute