(g*p)*-Closed Sets In Topological Spaces

Paulin mary Helen M; Anitha.P

doi:https://doi.org/10.14445/22315373/IJMTT-V6P508

International Journal of Mathematics Trends and Technology

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Volume 6 | Number 1 | Year 2014 | Article Id. IJMTT-V6P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V6P508

(gp)-Closed Sets In Topological Spaces

Paulin mary Helen M , Anitha.P

Abstract

In this paper, we have introduced a new class of sets called (g*p)*-closed sets which is properly placed in between the class of closed sets and the class of g-closed sets. As an application, we introduce two new spaces namely, gTp and gTp* spaces. We have also introduced (g*p)*-continuous and (g*p)*-irresolute maps and their properties are investigated.

Keywords

(g*p)*-closed sets, (g*p)*-continuous maps, (g*p)*-irresolute maps and gTp and gT*p spaces

References

1. D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38(1) (1986), 24-32.
2. 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.Sundram and H.Maki, On generlized continuous maps in tolopoligal spaces, Mem.Fac.Kochi Unvi.Ser.A, Math., 12 (1991), 5-13.
5. 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.
6. R. Devi, K. Balachandran and H. Maki, 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- pre open sets, Mem. Fac. Sci. Kochi Ser. A. Math., 16 (1995), 35-48.
8. Y.Gnanambal, On generalized pre regular closed sets in topological spaces, Indian J. Pure. Appl. Math., 28(3) (1977), 351-360.
9. N.Levine, Generalized closed sets in 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, R. Devi and K. Balachandran, Associated topologies of generalized α-closed and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A, Math., 15 (1994), 51-63.
12. H. Maki, J.Umehara and T.Noiri, Every topological space is pre - , Mem.Fac. Sci. Kochi Univ. Ser. A. Math., 17 (1996), 33-42.
13. A.S.Mashhour, M.E.Abd E1-Monsef and S.N.E1-Deeb, on pre-continuous and weak pre-continuous mappings, Proc.Math.and Phys.Soc.Egypt., 53(1982), 47-53.
14. O.Njastad, on some classes of nearly open sets, Pacific J.Math., 15 (1965), 961-970.
15. N.Palaniappan and K.C.Rao, Regular generalized closedsets,Kyungpook Math .J., 33(2) (1993), 211-219.
16. M.K.R.S.Veerakumar,between closed sets and g-closed sets, Mem.Fac.Kochi Unvi.Ser.A, Math., 17 (1996), 33-42.
17. N.Nagaveni, studies on generization of Homeomorphisms in topological spaces,ph.D.Thesis-Bharathiyar University ,July 1999.
18. M.Stone.Trans.Amer.Math .Soc.41 (1937), 374-481.

Citation :

Paulin mary Helen M , Anitha.P, "(g*p)*-Closed Sets In Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 6, no. 1, pp. 87-97, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V6P508