On the topology of $\delta_e$-open sets
الموضوعات :
C. ‎Dalk{\i}ran
1
,
M. ‎\"{O}zko\c{c}
2
1 - M\u{g}ula S{\i}tk{\i} Ko\c{c}man University, Graduate School of Natural and Applied Sciences, Mathematics, 48000, Mente\c{s}e-Mu\u{g}la, Turkey
2 - M\u{g}ula S{\i}tk{\i} Ko\c{c}man University, Faculty of Science, Department of Mathematics, 48000, Mente\c{s}e-Mu\u{g}la, Turkey
الکلمات المفتاحية: $\delta_e$-open, $\delta_e$-continuity, $\delta_e$-Hausdorff space, $\delta_e$-regular space, $\delta_e$-normal space,
ملخص المقالة :
The main purpose of this paper is to introduce and investigate a new class of open sets called $\delta_e$-open sets. For this aim, first we define and study the notion of $e$-regular open set via $e$-closure operator. Then, we introduce the notion of $\delta_e$-open set via $e$-regular open set. Several fundamental properties of the notion of $\delta_e$-open set have been revealed. Also, we show that the family of $\delta_e$-open sets is a topology strictly weaker than $\tau^{\delta}$ and stronger than $\tau$. In addition, we investigate relationships between the notion of $\delta_e$-open set and other existing notions in topology such as open sets, regular open sets and $\delta$-open sets. Furthermore, we give not only various properties and characterizations but also examples and counterexamples. Finally, some properties related to separation axioms are revealed.
[1] D. Akaln, M. Özkoc, Some new results concerning e-θ-open sets, J. Linear. Topol. Algebra. 11 (4) (2022), 279-292.
[2] S. Al Ghour, B. Irshedat, The topology of θw-open sets, Filomat. 31 (16) (2017), 5369-5377.
[3] H. H. Al-Jarrah, A. Al-Rawshdeh, E. M. Al-Saleh, K. Y. Al-Zoubi, Characterizations of RωO(X) sets by using δω-cluster points, Novi. Sad. J. Math. 2 (2019), 109-122.
[4] B. S. Ayhan, Mathematical structures via e-open sets, J. Linear, Topol. Algebra. 11 (3) (2022), 205-213.
[5] B. S. Ayhan, M. Özkoc, On almost contra e∗θ-continuous functions, Jordan. J. Math. Stat. 11 (4) (2018), 383-408.
[6] B. S. Ayhan, M. Özkoc, On contra e∗θ-continuous functions, Divulg. Mat. 19 (2) (2018), 1-13.
[7] E. Ekici, A note on a open sets and e∗-open sets, Filomat. 22 (2008), 89-96.
[8] E. Ekici, On e-open sets, DP∗-sets and DPE∗-sets and decompositions of continuity, Arab. J. Sci. Eng. 33 (2A) (2008), 269-281.
[9] H. Hdeib, w-closed mappings, Rev. Colomb. Mat. 16 (1982), 65-78.
[10] M. Özkoc, B. S. Ayhan, On characterizations of weakly e∗-continuity, Divulg. Mat. 21 (1-2) (2020), 9-20.
[11] M. Özkoc, B. S. Ayhan, On weakly eR-open functions, J. Linear. Topol. Algebra. 5 (3) (2016), 145-153.
[12] M. Özkoc, K. S. Atasever, On some forms of e∗-irresoluteness, J. Linear. Topol. Algebra. 8 (1) (2019), 25-39.
[13] M. Özkoc, T. Yılmaz, On characterizations of weakly e-irresolute functions, J. Linear. Topol. Algebra. 7 (1) (2018), 11-19.
[14] P. Sasmaz, M. Özkoc, On the topology δω-open sets and related topics, Konuralp. J. Math. 10 (1) (2022), 203-209.
[15] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481.
[16] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Trans. 78 (1968), 103-118.
