On Some Functions Related to e*-θ-open Sets

Year 2024, Volume: 5 Issue: 2, 72 - 82, 31.07.2024

Burcu Sünbül Ayhan

https://doi.org/10.54974/fcmathsci.1353956

Abstract

In this study, we defined the concept of quasi $e^*$-$\theta$-closed sets by means of $e^*$-$\theta$-open sets. Depending on this concept, we introduced approximately $e^{\ast}\theta$-open functions and investigated some of its basic properties. Also, we defined and studied contra pre $e^{\ast}\theta$-open functions, which are stronger than the approximately $e^{\ast}\theta$-open functions. Moreover, we characterized the class of $e^*\theta$-$T_\frac {1}{2}$ spaces.

Keywords

$e^*\theta$-open functions, quasi $e^*$-$\theta$-closed sets, approximately $e^*\theta$-open functions, contra pre $e^{\ast}\theta$-open functions, $e^* \theta$-$T_{\frac{1}{2}}$ spaces

Supporting Institution

Turkish-German University

Project Number

2021BR01

Thanks

This study was supported by Turkish-German University Scientifc Research Projects Commission under the grant no: 2021BR01. The author is very grateful to the Referees for the constructive comments and recommendations.

References

• Akalın D., Some Results on e-θ -Open and e∗ -θ -Open Sets, M. Sc. Thesis, Muğla Sıtkı Koçman University, Muğla, Türkiye, 2023.
• Akalın D., Özkoç M., On e∗ -θ -D-sets and related topics, arXiv:2403.01604 [math.GN], 2024.
• Ayhan B.S., On e∗θ -regular and e∗θ -normal spaces, arXiv:2407.07927 [math.GM], 2024.
• Ayhan B.S., On weakly e∗θ -open functions and their characterizations, Turkish Journal of Mathematics and Computer Science, 14(1), 56-65, 2022.
• Ayhan B.S., Özkoç M., On almost contra e∗ -continuous functions, Jordan Journal of Mathematics and Statistics, 11(4), 383-408, 2018.
• Ayhan B.S., Özkoç M., On contra e∗θ -continuous functions, Divulgaciones Matematicás, 19(2), 1-13, 2018.
• Caldas M., Jafari S., On some maps concerning gβθ -open sets, Proyecciones: Journal of Mathematics, 34(1), 15-24, 2015.
• Ekici E., New forms of contra continuity, Carpathian Journal of Mathematics, 24(1), 37-45, 2008.
• Ekici E., On e∗ -open sets and (D,S)∗ -sets, Mathematica Moravica, 13(1), 29-36, 2009.
• Farhan A.M., Yang X.S., New types of strongly continuous functions in topological spaces via δ -β -open sets, European Journal of Pure and Applied Mathematics, 8(2), 185-200, 2015.
• 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 International Scientific Conference on Pure Science, 1-10, 2019.
• Noiri T., Weak and strong forms of β -irresolute functions, Acta Mathematica Hungarica, 99, 315-328, 2003.
• Park J.H., Strongly θ -b -continuous functions, Acta Mathematica Hungarica, 110(4), 347-359, 2006.
• Rajesh N., Salleh Z., Some more results on b -θ -open sets, Buletinul Academiei de Stiinte a Republicii Moldova Matematica, 3(61), 70-80, 2009.
• Stone M.H., Applications of the theory of Boolean rings to general topology, Transactions of the American Mathematical Society, 41, 375-381, 1937.
• Velic̆ko N.V., H-closed topological spaces, American Mathematical Society Translations, 78(2), 103- 118, 1968.