# Strong Insertion of a Contra-Continuous Function Between Two Comparable Contra-B−Continuous Functions

### Abstract

Enough condition in terms of lower cut sets are given for the strong insertion of a contra-continuous function between two comparable contra-b−continuous real-valued functions on such topological spaces that kernel of sets is open.

### 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.

D. Andrijevic, On b-open sets, Mat. Vesnik., 48 (1996), 59-64.

F. Brooks, Indefinite cut sets for real functions, Amer. Math. Monthly,

(1971), 1007-1010.

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

H. H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math., 8 (1964), 351-360.

J. Dontchev, The characterization of some peculiar topological space via

α− and β−sets, Acta 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),

-137.

E. Ekici, New forms of contra-continuity, Carpathian J. Math.,

(1)(2008), 37-45.

A. A. El-Atik, A study of some types of mappings on topological spaces, M. Sc. Thesis, Tanta Univ., (1997).

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. Katˇetov, On real-valued functions in topological spaces, Fund. Math.,

(1951), 85-91.

M. Katˇetov, 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),

-190.

N. Levine, Semi-open sets and semi-continuity in topological space, Amer. Math. Monthly, 70 (1963), 36-41.

S. N. Maheshwari and R. Prasad, On ROs −spaces, Portugal. Math.,

(1975), 213-217.

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

A. S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deeb, On pre- continuous and weak pre-continuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53.

M. Mirmiran, Weak insertion of a contra-Baire-1 (Baire-.5) function, MATLAB Journal, 1(1)(2018), 9-13.

M. Mrsevic, On pairwise R and pairwise R1 bitopological spaces, Bull.

Math. Soc. Sci. Math. R. S. Roumanie, 30(1986), 141-145.

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

M. Przemski, A decomposition of continuity and α−continuity, Acta

Math. Hungar., 61(1-2)(1993), 93-98.

Copyright (c) 2018 MathLAB Journal

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.