New maximal and minimal sets via βθ-open sets

• Autorzy: Caldas M. , Jafari S. , Noiri T.

Identyfikatory

DOI

10.1515/fascmath-2018-0014

• Języki publikacji: EN

Abstrakty

EN

Nakaoka and Oda ([9] and [10]) introduced the notion of maximal open sets and minimal closed sets. In this paper, we introduce new classes of sets called maximal βθ-open sets, minimal βθ-closed sets, βθ-semi maximal open sets and βθ-semi minimal closed sets and investigate some of their fundamental properties.

Słowa kluczowe

EN

topological space; maximal open set; minimal closed set; βθ-open set; βθ-semi maximal open set

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 61
• Strony: 17--25
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Caldas M.

• Departamento de Matemótica Aplicada Universidade Federal Fluminense Rua Mário Santos Braga, s/n° 24020-140, Niterói, RJ Brasil

autor

Jafari S.

• College of Vestsjaelland South Herrestraede 11 4200 Slagelse, Denmark

autor

Noiri T.

• 2949-1 Shiokita-cho Hinagu, Yatsushiro-shi Kumamoto-ken, 869-5142 Japan

Bibliografia

• [1] El-Monsef M.E.Abd., EL-Deeb S.N., Mahmoud R.A., β-open and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.
• [2] Andrijević D., Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
• [3] Caldas M., On θ-β-generalized closed sets and θ-β-generalized continuity in topolological spaces, J. Adv. Math. Studies, 4(2011), 13-24.
• [4] Caldas M., Weakly sp-θ-closed functions and semipre-Hausdorff spaces, Creative Math. Inform., 20(2)(2011), 112-123.
• [5] Caldas M., Jafari S., New notions via β-θ-closed sets, Selected papers of the 2010 International Conference on Topology and its Applications, Dimitris Georgiou, Stavros Iliadis, Ioannis Kougias (Guest Editors of the special volume), 34-44.
• [6] Caldas M., Other characterizations of β-θ-R0 topological spaces, Tamkang J. Math., 49(3)(2013), 303-312.
• [7] Caldas M., On contra βθ-continuous functions, Proyecciones Journal Math., 39(4)(2013), 333-342.
• [8] Ekici E., Noiri T., On separation axioms and sequences, Math. Moravica, 11(2007), 39-46.
• [9] Nakaoka F., Oda N., Some applications of minimal open sets, Int. J. Math. Math. Sci., 27(2001), 471-476.
• [10] Nakaoka F., Oda N., Some properties of maximal open sets, Int. J. Math. Math. Sci., 21(2003), 1331-1340.
• [11] Noiri T., Weak and strong forms of β-irresolute functions, Acta Math. Hungar., 99(2003), 315-328.
• [12] Veličko N.V., H-closed topological spaces, 70(1966), 98-112; English transl., in Amer. Math. Soc. Transl. (2), 78(1968), 103-118.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).