Mathematical structures via $e$-open sets
الموضوعات :
B. Ayhan
1
(Quality Management Unit, Rectorate, Turkish-German University, 34820, Beykoz-Istanbul, Turkey)
الکلمات المفتاحية: $e$-open set, $e$-kernel, $\Lambda$-set, $\lambda$-closed set, $\lambda$-derived set,
ملخص المقالة :
Considering the $e$-kernel defined by \"{O}zko\c{c} and Ayhan [18] in a topological space, a new type of generalized closed set is studied through this article. The aim of this paper is to introduce a new class of sets called $ge\Lambda$-closed sets and $ge\Lambda$-open sets in a topological space and to study their properties and characterizations.
[1] D. Andrijevic, On b-open sets, Mat. Vesnik. 48 (1996), 59-64.
[2] F. G. Arenas, J. Dontchev, M. Ganster, On λ-sets and the dual of generalized continuity, Questions Answers Gen. Topology. 15 (1) (1997), 3-13.
[3] P. Bhattacharyya, B. K. Lahiri, On semi-generalized closed sets in topology, Indian J. Math. 29 (3) (1987), 375-382.
[4] M. Caldas, S. Jafari, On some low separation axioms via λ-open and λ-closure operator, Rend. Circ. Mat. Palermo. 54 (2) (2005), 195-208.
[5] M. Caldas, S. Jafari, G. Navalagi, More on λ-closed sets in topological spaces, Rev. Colombiana Mat. 41 (2) (2007), 355-369.
[6] M. Caldas, S. Jafari, T. Noiri, On Λ-generalized closed sets in topological spaces, Acta. Math. Hungar. 118 (4) (2008), 337-343.
[7] M. Caldas, S. Jafari, T. Noiri, On Λb-sets and the associated topology τΛb, Acta. Math. Hungar. 110 (4) (2006), 337-345.
[8] J. Dontchev, On door spaces, Indian J. Pure Appl. Math. 26 (9) (1995), 873-881.
[9] E. Ekici, On e-open sets, DP∗-sets and DPE∗-sets and decompositions of continuity, Arabian J. Sci. Eng. 33 (2A) (2008), 269-282.
[10] E. Ekici, On R-spaces, Int. J. Pure App. Math. 25 (2) (2005), 163-172.
[11] V. Iyer, K. Shrivastava, Characterizations of a partitiion topology on a set, Int. J. Pure Appl. Math. 74 (3) (2012), 313-320.
[12] M. K. R. S. VeeraKumar, g∗-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. Math. 21 (2000), 1-19.
[13] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo. 19 (2) (1970), 89-96.
[14] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly. 70 (1963), 36-41.
[15] H. Maki, Generalized Λ-sets and the associated closure operator, The Special Issue in Commemoration of Prof. Kazusada IKEDAs Retirement. (1986), 139-146.
[16] S. P. Missier, V. H. Raj, gsΛ-closed sets in topological spaces, Int. J. Gen. Topology, 5 (2012), 33-44.
[17] S. Modak, J. Hoque, Mathematical structures via b-open sets, Trans. A. Razmadze Math. Ins. 176 (1) (2022), 73-81.
[18] M.Özko¸ c, B. S. Ayhan, On Λe-sets and Ve-sets and the associated topology τΛe, Gen. Math. Notes. 32 (1) (2016), 1-11.
[19] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-381.
[20] P. Sundaram, M. S. John, On ω-closed sets in topology, Acta. Ciencia. Indica Math. 26 (4) (2000), 389-392.
[21] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Trans. 78 (2) (1968), 103-118.
