Proyecciones Journal of Mathematics
Vol. 28, N° 2, pp. 111-123, August 2009.
Universidad Católica del Norte
Antofagasta - Chile


θ-GENERALIZED SEMI-OPEN AND θ-GENERALIZED SEMI-CLOSED FUNCTIONS


Govindappa Navalagi¹
Md. Hanif Page²

¹ B. V. B. College Of Eng. And Tech., India
² G. H College, India


Correspondencia a:

Abstract

In this paper, we introduce and study the notions of θ-generalized-semi-open function, θ-generalized- semi-closed function,pre θ-generalized-semi-open function,pre θ-generalized-semi-closed function, contra pre θ-generalized-semi-open, contra pre θ-generalized-semi-do sed function and θ-generlized-sem-homeomorphism in topological spaces and study their properties.

2000 Mathematics Subject Classification : 54A05, 51C10, 54D10; Secondary: 54C08

Keywords : θgs-closed, θgs-open, pre θgs-open, pre θgs-closed , θgs-closed function, θgs-open function, θgs-homeomorphism, θgsc-homeomorphism.

References

[1] S. P. Arya and T. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math., 21, pp. 717-719, (1990).        [ Links ]

[2] K. Balachandran, P. Sundaram and H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi. Uni. Ser.A (Math.), 12, pp. 5-13, (1991).        [ Links ]

[3] P. Bhattacharya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math.,29 (3), pp. 375-382, (1987).        [ Links ]

[4] M. Caldas and S. Jafri, On θ-semi generalized closed sets in topology, Kyngpook Math. J., 43, pp. 135-148, (2003).        [ Links ]

[5] S. G. Crossely and S.K. Hildbrand, On semi-closure. Texas J. Sci, 22, pp. 99-112, (1971).        [ Links ]

[6] R. Devi , K. Balachandran and H. Maki, Semi-generalized and generalized semi maps, Mem. Fac. Sci. Kochi. Uni. Ser. A (Math.), 14, pp. 41-54, (1993).        [ Links ]

[7] G. Di Maio, T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math., 18, pp. 226-233, (1987).        [ Links ]

[8] J. Dontechev and H. Maki, On θ-generalized closed sets, Internat. J. Math.and Math. Sci. 22, pp. 239-249, (1999).        [ Links ]

[9] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer.Math. Monthly 70, pp. 36-41, (1963).        [ Links ]

[10] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19, pp. 89-96, (1970).        [ Links ]

[11] H. Maki, P. Sundarani and K. Balachandran, On generalized homeomorphismsin topological spaces, Bull. Fukuoka Univ. Ed. III , 40 (1991).        [ Links ]

[12] Govindappa Navalagi and Md. Hanif Page, On θgs-Neighbiurhoods, accepted for publication, Indian Journal of Mathematics and Mathematical Sciences, Vol. 2, 2 (Dec.2007).        [ Links ]

[13] Govindappa Navalagi and Md. Hanif Page, On some more properties of θgs- Neighbiurhoods (Communicated).        [ Links ]

[14] Govindappa Navalagi and Md. Hanif Page, On θgs-continuity and θgs-irresoluteness (Communicated).        [ Links ]

[15] Govindappa Navalagi and Md. Hanif Page, On some separation axioms via θgs- open sets (Communicated).        [ Links ]

[16] N. V. Velicko, On H-closed topological spaces, Amer. Math. Soc. Transí., 78, pp. 103-118, (1968).        [ Links ]

GOVINDAPPA NAVALAGI
Department of Mathematics
KLE Society's
G. H. College
Haveri-581 110
Karnataka
INDIA
e-mail : gnavalagi@hotmail.com

Received : March 2008. Accepted : March 2009