Insertion of a contra-Baire-1 (Baire-.5) function

• Majid Mirmiran Department of Mathematics, University of Isfahan
• Binesh Naderi School of Management and Medical Information, Medical University of Isfahan

Keywords: Insertion, strong binary relation, Baire-.5 function, kernel of sets, lower cut set

Abstract

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a Baire-.5 function between two comparable real-valued functions on the topological spaces that $F_{\sigma}$-kernel of sets are $F_{\sigma}$-sets.

References

A. Al-Omari and M.S. Md Noorani. Some properties of contra-b-continuous and almost contra-b-continuous functions, European J. Pure. Appl. Math., 2(2) (2009), 213–230.

F. Brooks. Indefinite cut sets for real functions. Amer. Math. Monthly, 78(1971), 1007–1010.

M. Caldas and S. Jafari. Some properties of contra-β−continuous functions. Mem. Fac. Sci. Kochi. Univ., 22(2001), 19–28.

J. Dontchev. The characterization of some peculiar topological space via α− and β−sets.nActa Math. Hungar., 69(1-2) (1995), 67–71.

J. Dontchev. Contra-continuous functions and strongly S-closed space. Intrnat. J. Math. Math. Sci., 19(2) (1996), 303–310.

J. Dontchev and H. Maki. On sg-closed sets and semi−λ−closed sets. Questions Answers Gen. Topology, 15(2) (1997), 259–266.

E. Ekici. On contra-continuity. Annales Univ. Sci. Bodapest, 47 (2004), 127–137.

E. Ekici. New forms of contra-continuity. Carpathian J. Math., 24(1) (2008), 37–45.

A.I. El-Magbrabi. Some properties of contra-continuous mappings. Int. J. General Topol., 3(1-2) (2010), 55–64.

M. Ganster and I. Reilly. A decomposition of continuity. Acta Math. Hungar., 56(3-4) (1990), 299–301.

S. Jafari and T. Noiri. Contra-continuous function between topological spaces. Iranian Int. J. Sci., 2 (2001), 153–167.

S. Jafari and T. Noiri. On contra-precontinuous functions, Bull. Malaysian Math. Sc. Soc., 25 (2002), 115–128.

M. Katětov. On real-valued functions in topological spaces. Fund. Math., 38 (1951), 85–91.

M. Katětov. Correction to, ”On real-valued functions in topological spaces”. Fund. Math., 40 (1953), 203–205.

E. Lane. Insertion of a continuous function. Pacific J. Math., 66 (1976), 181–190.

H. Maki. Generalized Λ−sets and the associated closure operator, The special Issue in commemoration of Prof. Kazuada IKEDA’s Retirement, (1986), 139–146.

S. N. Maheshwari and R. Prasad On R Os -spaces. Portugal. Math., 34 (1975), 213–217.

M. Mirmiran. Insertion of a function belonging to a certain subclass of R X . Bull. Iran. Math. Soc., Vol. 28, No. 2 (2002), 19–27.

M. Mrsevic. On pairwise R and pairwise R 1 bitopological spaces. Bull. Math. Soc. Sci. Math. R. S. Roumanie, 30 (1986), 141–145.

A.A. Nasef. Some properties of contra-continuous functions. Chaos Solitons Fractals, 24 (2005), 471–477.

M. Przemski. A decomposition of continuity and α−continuity. Acta Math. Hungar., 61(1-2) (1993), 93–98.

H. Rosen. Darboux Baire-.5 functions. Proceedings of The American Mathematical Society, 110(1) (1990), 285–286.

M.H. Stone. Boundedness properties in function-lattices. Canad. J. Math.,1 (1949), 176–189.