Some new results concerning $e\text{-}\theta\text{-}$open sets

Subject Areas : General topology

D. Akalin ¹ , M. Özkoc ²

1 - Department of Mathematics, Graduate School of Natural and Applied Sciences, Mu\v{g}la S{\i}tk{\i} Ko\c{c}man University, 48000, Mente\c{s}e-Mu\v{g}la, Turkey
2 - Department of Mathematics, Faculty of Science, Mu\v{g}la S{\i}tk{\i} Ko\c{c}man University, 48000, Mente\c{s}e-Mu\v{g}la, Turkey

Received: 2022-11-24 Accepted : 2022-12-29 Published : 2022-12-01

Keywords: $e$-$theta$-open set, $e$-open set, $e$-$\theta$-closed set, $e$-$\theta$-closure,

Abstract :

‎The main purpose of this paper is to study the class of $e\text{-}\theta$-open sets and explore some of their new properties‎. ‎Also‎, ‎we introduce and study some weak separation axioms by utilizing $e\text{-} \theta$-open sets‎. ‎In addition‎, ‎we define the notion of $e\text{-}\theta\text{-}$kernel and slightly $e\text{-}\theta\text{-}R_0$ spaces‎. ‎Furthermore‎, ‎we apply them to discuss some fundamental properties of the graph functions‎. ‎We obtain not only some characterizations but also many new results‎.

References:

[1] D. Andrijevic, On b-open sets, Matematicki Vesnik. 48 (1996), 59-64.

[2] M. Caldas, S. Jafari, T. Noiri, On The Class of Semipre-θ-open Sets in Topological Spaces, Selected papers of the 2014 International Conference on Topology and its Applications, (2015), 49-59.

[3] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat. 21 (2) (2007), 31-44.

[4] E. Ekici, On e∗-open sets and (D,S)∗-sets, Math. Morav. 13 (2009), 29-36.

[5] S. Jafari, T. Noiri, On strongly θ-semi-continuous functions, Indian J. Pure. Appl. Math. 29 (1998), 1195-1121.

[6] T. Noiri, Strongly θ-precontinuous functions, Acta. Math. Hungar. 90 (2001), 307-316.

[7] T. Noiri, V. Popa, Strongly θ-β-continuous functions, J. Pure. Math. 19 (2002), 31-39.

[8] M. Ozkoc, G. Aslim, On characterizations of weakly e-irresolute functions, J. Linear. Topol. Algeb. 7 (1) (2018), 11-19.

[9] M. Ozkoc, G. Aslim, On strongly θ-e-continuous functions, Bull. Korean. Math. Soc. 47 (5) (2010), 1025-1036.

[10] J. H. Park, Strongly θ-b-continuous functions, Acta. Math. Hungar. 110 (4) (2006), 347-359.

[11] N. Rajesh, Z. Salleh, Some more results on b-θ-open sets, Buletinul Academiei de Stiinte a Moldovei. Matematica. 3 (61) (2009), 70-80.

[12] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-381.

[13] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968), 103-118.