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On weakly \(e^*\)-open and weakly \(e^*\)-closed functions. (English) Zbl 1463.54049

Summary: The aim of this paper is to introduce and study two new classes of functions called weakly \(e^*\)-open functions and weakly \(e^*\)-closed functions via the concept of \(e^*\)-open set defined by E. Ekici [Math. Morav. 13, No. 1, 29–36 (2009; Zbl 1265.54072)]. 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 M. Caldas and G. Navalagi [An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 49, No. 1, 115–128 (2003; Zbl 1059.54501)], respectively. Moreover, we investigate not only some of their fundamental properties, but also their relationships with other types of existing topological functions.

MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54C05 Continuous maps
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[1] M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud,β-open sets andβ-continuous mappings, Bull Fac Sci Assiut Univ. 12 (1983), 77-90.
[2] B. S. Ayhan, M. ¨Ozko¸c, Almoste∗-continuous functions and their characterizations, J. Nonlinear Sci. Appl. 9 (2016), 6408-6423. · Zbl 1378.54018
[3] C. W. Baker, Contra-open functions and contra-closed functions, Math. Today. 15 (1997), 19-24. · Zbl 0903.54008
[4] C. W. Baker, Decomposition of opennes, Internat. J. Math. and Math. Sci. 17 (1994), 413-415. · Zbl 0798.54018
[5] N. Biswas, On some mappings in topological spaces, Bull. Calcutta Math. Soc. 61 (1969), 127-135. · Zbl 0215.51605
[6] M. Caldas, G. Navalagi, On weak forms ofβ-open andβ-closed functions, Anal. St. Univ. Al. I. Cuza, Iasi. Mat. 49 (2003), 115-128. · Zbl 1059.54501
[7] E. Ekici, A note ona-open sets ande∗-open sets, Filomat. 22 (2008), 89-96. · Zbl 1199.54007
[8] E. Ekici, Ona-open sets,A∗-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Budapest. Sect. Math. 51 (2008), 39-51. · Zbl 1224.54031
[9] E. Ekici, One∗-open sets and (D,S)∗-sets, Math. Morav. 13 (2009), 29-36. · Zbl 1265.54072
[10] E. Ekici, New forms of contra continuity, Carpathian J. Math. 24 (2008) 37-45. · Zbl 1174.54346
[11] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat. 21 (2) (2007), 31-44. · Zbl 1141.54006
[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. · Zbl 0524.54016
[13] N. Levine, Strong continuity in topological space, Amer. Math. Monthly. 67 (1960), 269. · Zbl 0156.43305
[14] R. A. Mahmoud, M. E. Abd El-Monsef,β-irresolute andβ-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. · Zbl 0571.54011
[16] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970. · Zbl 0137.41903
[17] T. Noiri, Properties of hyperconnected space, Acta Math. Hung. 66 (1995), 147-154. · Zbl 0818.54020
[18] M. ¨Ozko¸c, B. S. Ayhan, On weaklyeR-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. · Zbl 0562.54020
[20] D. A. Rose, D. S. Jankovic, Weakly closed functions and Hausdorff spaces, Math. Nachr. 130 (1987), 105-110. · Zbl 0622.54008
[21] M. K. Singal, A. R. Singal, Almost continuous mappings, Yokohama Math. J. 16 (1968), 63-73. · Zbl 0191.20802
[22] M. H. Stone, Aplications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481. · JFM 63.1173.01
[23] N. V. Veli˘cko,H-closed topological spaces, Amer. Math. Soc. Trans. 78 (1968), 103-118.
[24] S. Willard, General Topology, Addition Wesley Publishing Company, 1970.
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