On weakly eR-open functions

Subject Areas : History and biography

M.  Ozkoc ¹ (Department of Mathematics, Faculty of Science Mu˘gla Sıtkı Ko¸cman University, Mente¸se-Mu˘gla 48000, Turkey)
B. S.  Ayhan ² (Department of Mathematics, Faculty of Science Mu˘gla Sıtkı Ko¸cman University, Mente¸se-Mu˘gla 48000, Turkey)

Received: 2016-03-28 Accepted : 2016-06-30 Published : 2016-09-01

Keywords: $e$-closed set, weakly $eR$-open function, $e$-$theta$-open set, $e$-$theta$-open function,

Abstract :

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$\theta$-open sets and $e$-$\theta$-closure operator which are defined by Ozkoc and Aslım [10] called weakly $eR$-open functions and $e$-$\theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topological functions.

References:

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

[2] M. Caldas, E. Ekici, S. Jafari, R.M. Latif, On weakly BR-open functions and their characterizations in topological spaces. Demonstratio Math., 44 (1) (2011), 159-168.

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

[4] ------, On e-open sets, DP*-sets and DPE*-sets and decompositions of continuity. Arab. J. Sci. Eng. Sect. A Sci., 33 (2) (2008), 269-282.

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

[6] ------, Strong continuity in topological spaces. Amer. Math. Monthly., 67 (1960), 269.

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

[8] O. Njastad, On some classes of nearly open sets. Pacic J. Math., 15 (1965), 961-970.

[9] T. Noiri, A generalization of closed mappings. Atti. Accad. Naz. Lince Rend. Cl. Sci. Fis. Mat. Natur., 8 (1973), 210-214.

[10] M. Ozkoc and G. Aslm, On strongly -e-continuous functions. Bull. Korean Math. Soc., 47 (5) (2010), 1025-1036.

[11] J.H. Park, Strongly *-b-continuous functions. Acta Math. Hungar., 110 (4) (2006), 347-359.

[12] M. Stone, Application of the theory of Boolean ring to general topology. Trans. Amer. Math. Soc., 41 (1937), 374-481.

[13] N.V. Velicko, H-closed topological spaces. Amer. Math. Soc. Transl., 78 (1968), 103-118.