On weakly e*-open and weakly e*-closed Functions
الموضوعات :
1 - Mugla Sitki Kocman University, Faculty of Science, Department of Mathematics, 48000, Mentese-Mugla, Turkey
2 - Mugla Sitki Kocman University, Graduate School of Natural and Applied Sciences, Mathematics, 48000, Mentese- Mugla, Turkey
الکلمات المفتاحية: $e^{*}$-open set, $e^{*}$-open function, weakly $e^{*}$-open function, weakly $e^{*}$-closed function, contra $e^{*}$-closed,
ملخص المقالة :
The aim of this paper is to introduce and study two new classes offunctions called weakly $e^{*}$-open functions and weakly$e^{*}$-closed functions via the concept of $e^{*}$-open set definedby Ekici \cite{erd1}. The notions of weakly $e^{*}$-open and weakly$e^{*}$-closed functions are weaker than the notions of weakly$\beta$-open and weakly $\beta$-closed functions defined by Caldasand Navalagi \cite{cal}, respectively. Moreover, we investigate notonly some of their fundamental properties, but also theirrelationships with other types of existing topological functions.
[1] M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, β-open sets and β-continuous mappings, Bull Fac Sci Assiut Univ. 12 (1983), 77-90.
[2] B. S. Ayhan, M.Özkoc, Almost e∗-continuous functions and their characterizations, J. Nonlinear Sci. Appl. 9 (2016), 6408-6423.
[3] C. W. Baker, Contra-open functions and contra-closed functions, Math. Today. 15 (1997), 19-24.
[4] C. W. Baker, Decomposition of opennes, Internat. J. Math. and Math. Sci. 17 (1994), 413-415.
[5] N. Biswas, On some mappings in topological spaces, Bull. Calcutta Math. Soc. 61 (1969), 127-135.
[6] M. Caldas, G. Navalagi, On weak forms of β-open and β-closed functions, Anal. St. Univ. Al. I. Cuza, Iasi. Mat. 49 (2003), 115-128.
[7] E. Ekici, A note on a-open sets and e∗-open sets, Filomat. 22 (2008), 89-96.
[8] E. Ekici, On a-open sets, A∗-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Budapest. Sect. Math. 51 (2008), 39-51.
[9] E. Ekici, On e∗-open sets and (D,S)∗-sets, Math. Morav. 13 (2009), 29-36.
[10] E. Ekici, New forms of contra continuity, Carpathian J. Math. 24 (2008) 37-45.
[11] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat. 21 (2) (2007), 31-44.
[12] S. N. El-Deeb, I. A. Hasanein, A. S. Mashhour, T. Noiri, On p-regular spaces, Bull. Math. de la Soc. Sci. Math. de la R.S. Raumanie, 27 (1983), 311-315.
[13] N. Levine, Strong continuity in topological space, Amer. Math. Monthly. 67 (1960), 269.
[14] R. A. Mahmoud, M. E. Abd El-Monsef, β-irresolute and β-topological invariant, Proc. Pakistan Acad. Sci. 27 (1990), 285-296.
[15] A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt. 53 (1982), 47-53.
[16] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.
[17] T. Noiri, Properties of hyperconnected space, Acta Math. Hung. 66 (1995), 147-154.
[18] M.Özkoc, B. S. Ayhan, On weakly eR-open functions, J. Linear. Topological. Algebra. 5 (3) (2016), 145-153.
[19] D. A. Rose, On weak openness and almost openness, Internat. J. Math. and Math. Sci. 7 (1984), 35-40.
[20] D. A. Rose, D. S. Jankovic, Weakly closed functions and Hausdorff spaces, Math. Nachr. 130 (1987), 105-110.
[21] M. K. Singal, A. R. Singal, Almost continuous mappings, Yokohama Math. J. 16 (1968), 63-73.
[22] M. H. Stone, Aplications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481.
[23] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Trans. 78 (1968), 103-118.
[24] S. Willard, General Topology, Addition Wesley Publishing Company, 1970.
