On Weakly e*-θ-open Functions and Their Characterizations

Yıl 2022, Cilt: 14 Sayı: 1, 56 - 65, 30.06.2022

Burcu Sünbül Ayhan

https://doi.org/10.47000/tjmcs.1015626

Öz

The main aim of this paper is to introduce and study a new class of weakly open functions called weakly e*-θ-open functions via e*-θ-open sets [13], which is a stronger concept than weakly e*-open functions [22]. Moreover, we obtain various characterizations of weakly e*-θ-open functions and investigate some of their fundamental properties. In additon, we investigate not only the relationships of these functions with some othertypes of existing topological functions, but also several basic results related to connectedness, e*θ-connectedness [5] and hyperconnectedness [18].

Anahtar Kelimeler

e*-θ-open set, e*-θ-open function, e*θ-connectedness, e*θ-T2 space

Destekleyen Kurum

Türk-Alman Üniversitesi Bilimsel Araştırma Projeleri

Proje Numarası

2021BR01

Teşekkür

This study was supported by Turkish-German University Scientific Research Projects Commission under the grantno: 2021BR01.

Kaynakça

• Andrijevic, D., On b-open sets, Mat. Vesnik,48(1996), 59–64.
• Arya, S. P., Gupta R., Strongly continuous mappings, Kyungpook Math. J.,14(1974), 131–143.
• Ayhan, B. S., On e∗θ-regular and e*θ-normal spaces, Advances in Topology and its Structures: Foundations, Theory and Application, inreview.
• Ayhan, B. S., Özkoç ̧ M., On almost contra e*θ-continuous functions, Jordan J. Math. Stat., 11(4)(2018), 383–408.
• Ayhan, B. S., Özkoç ̧ M., On contra e*θ-continuous functions, Divulgaciones Matematicas, 19(2)(2018), 1–13.
• Caldas, M., Navalagi, G., On weak forms of preopen and preclosed functions, Archivum Mathematicum, 40(2004), 119–128.
• Caldas M., Navalagi G., On weak forms of semi-open and semi-closed functions, Missouri J. Math. Sci., 18(3)(2006), 165–178.
• Caldas, M., Ekici, E., Jafari, S., Latif, M., On weakly BR-open functions and their characterizations in topological spaces, DemonstratioMathematica, 44(1)(2011), 159-168.
• Ekici, E., On a-open sets, A*-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. E ̈otv ̈os Sect. Math., 51(2008), 39–51.
• Ekici, E., On e-open sets,DP*-sets and DPE*-sets and decompositions of continuity, Arabian J. Sci. Eng.,33(2A)(2008), 269–282.
• Ekici, E., New forms of contra-continuity, Carpathian J. Math., 24(1)(2008), 37–45.
• Ekici, E., On e*-open sets and(D,S)*-sets, Math. Morav., 13(1)(2009), 29–36.
• Farhan, A. M., Yang, X. S., New types of strongly continuous functions in topological spaces via δ-β-open sets, Eur. J. Pure Appl. Math., 8(2)(2015), 185–200.
• Jumaili, A. M. F. A., Abed, M. M., Sharqi, F. G. A., Other new types of mappings with strongly closed graphs in topological spaces via e-θ and δ-β-θ-open sets, The 1st Int. Sci. Conf. P. Sci., (2019), 1–10.
• Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36–41.
• Levine, N., Strong continuity in topological spaces, Amer. Math. Monthly, 67(1960), 269.
• Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47–53.
• Noiri, T., A generalization of closed mappings, Atti. Accad. Naz. Lince Rend. Cl. Sci. Fis. Mat. Natur.,8(1973), 210–214.
• Noiri, T., Omari, A. A., Noorani, M. S. M., Weak forms of open and closed functions via b-θ open sets, Demonstratio Mathematica, 42(2009), 193–203.
• Noiri, T., Omari, A. A., Noorani, M. S. M., Weakly b-open functions,Mathematica Balkanica, 23(2009), 1–13.
• Özkoç ̧, M., Ayhan, B.S., On weakly eR-open functions, J. Linear Topol. Algebra, 5(3)(2016), 145–153.
• Özkoç ̧, M., Erdem, S., On weakly e∗-open functions and weakly e*-closed functions, J. Linear Topol. Algebra, 9(3)(2020), 201–211.
• Rose, D. A., On weak openness and almost openness, Internat. J. Math. and Math. Sci., 7(1984), 35–40.
• Rose, D. A., Jankovic, D. S., Weakly closed functions and Hausdorff spaces, Math. Nachr., 130(1987), 105–110.
• Singal, M. K., Singal, A. R., Almost continuous mappings, Yokohama Math. J., 16(1968), 63–73.
• Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375–381.
• Velicko, N. V., H-closed topological spaces, Amer. Math. Soc. Transl., 78(2)(1968), 103–118.