Weakly Generalized Closed Map

Authors: R. Parimelazhagan, N. Nagaveni

Abstract:

In this paper we introduce a new class of mg-continuous mapping and studied some of its basic properties.We obtain some characterizations of such functions. Moreover we define sub minimal structure and further study certain properties of mg-closed sets.

Keywords: M-structure, mg-continuous mapping, minimal structure, mg T2 space, sub minimal structure, T12 space, mg-compact set.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072038

References:

[1] Andrijevic, D.Semi-preopen sets, Mat.Vesnik,38(1986),24-32.
[2] Arya,S.P.and Nour, T.Characterizatopms pf s-normal spaces, Indian J.Pure Appl.Math.21(1990),717-719.
[3] Balachandran, K.Sundaram,P.and Maki, H Generalized locally closed sets and GLC-continuous functions, Indian J.Pure. Appl. Math. 27(1996),235-244.
[4] Balachandran, K.Sundaram, P.and Maki, H. On generalized continuous maps in topological spaces, Mem. Fac.Sci. Kochi Univ. Math. 12 (1991),2-13.
[5] Bhattacharyya, P. and Lahiri, B.K. Semi-generalized closed sets in topology, Indian J.Math. 29(1987),376- 382.
[6] Cameron and Noiri, T.Almost irresolute functions Indian J.Pure Appl. Math. 20(1989),472-482.
[7] El-Deeb, N. Hasanein, I.A. Noiri, T. and Mashhour, A.S. On P-regular spaces, Bull. Math. Soc. Sci. Math.R.S Roumanie 27(1983), 311-319.
[8] Ganster, M.and Reilly, I.L. Locally closed sets and LC-continuous functions, Internat.J.Math.Sci., (12)(1989),417-424.
[9] Levine, N.Generalized closed setsin topology, Rend.Circ. Mat.Palwemo, 19(1970), 89-96.
[10] Levine, N.Semi-open sets and semi-continuity in topological spaces, Amer. Math.MOntly, 70(1963),36-41.
[11] Levine, N Strong continuity in topological spaces, Amer. Math.Monthly, 67 (1960), 269.
[12] Long, P.E. and Mcgehee, E.E.Jr. Properties of almost continuous functions, Proc. Amer.Math.Soc., 24(1970), 175-180.
[13] Mashhour, A.S,.Abd.El-Monsef, M.E. and Deeb, S.N. On pre continuous mappings and weak precontinuous mappings, Proc.Math, Phys. Soc Egypt., 53(1982),47-53.
[14] Mashhour, A.S.Hassanein, I.A. and El-Deeb, S.N.a - continuous and a -open mappings, Acta. Math. Hunger., 41(1983), 213-218.
[15] Nagaveni.N.Studies on generalizations of Homeomorphisms in topological spaces. Ph.D.,Thesios; Bharathiar University, Coimbatore 1999.
[16] Njastad, O.On some classes of nearly open sets, Pacific J.Math. 15(1965), 961-970.
[17] Noiri, T.A generalization of closed mapping, Atti Acad. Naz. Linceei Rend. Cl.Sci.Fis. Mat. Natur., 54(1973)412-415.
[18] Stone .M.Application of the theory of Boolean rings to general topology, Trans. Amer.Math.Soc., 41(1937), 374-481.
[19] Sundaram, P. Studies on Generaliztions of continuous maps in topological spaces, Ph.D., Thesis, Bharathiar University, Coimbatore (1991).