Some Functions via Delta-Semiopen Sets

Yıl 2017, Cilt: 43 Sayı: 2, 189 - 197, 31.10.2017

Yusuf Beceren

Öz

In this paper, it is introduced and studied new
classes of generalizations of some non-continuous functions concerning the
concepts of weak forms of d-semiopen sets in topological spaces. And also it is
given some of their properties.

Anahtar Kelimeler

α-open set, Semiopen set, Preopen set, β-open set

Delta-Yarıaçık Kümelerle Bazı Fonksiyonlar

Öz

Bu makalede, topolojik
uzaylarda d-yarıaçık kümelerin zayıf kavramlarıyla bazı sürekli
olmayan fonksiyonların yeni genelleştirmeleri ortaya konuldu ve çalışıldı. Aynı
zamanda, bu fonksiyonların sağladığı bazı özellikler verildi.

Anahtar Kelimeler

Yarıaçık küme, Önaçık küme, α-açık küme, β-açık küme

Kaynakça

• Abd El-Monsef ME, El-Deeb SN and Mahmoud RA (1983). β-open sets and β-continuous mapping. Bull. Fac. Sci. Assiut Univ. A 12: 77-90.
• Al-Nashef B (2002). A decomposition of α-continuity and semi-continuity. Acta Math. Hungar. 97: 115-120.
• Beceren Y, Noiri T, Fidancı MC and Arslan K (2006). On some generalizations of locally closed sets and lc-continuous functions. Far East J. Math. Sci. (FJMS) 22: 333-344.
• Beceren Y and Noiri T (2008). Some functions defined by semi-open and β-open sets. Chaos Solitons Fractals 36: 1225-1231.
• Bourbaki N (1966). Elements of Mathematics, General Topology. Part 1. Hermann, Addison-Wesley Publishing Co., Reading, Mass., Paris.
• Caldas M, Georgiou DN, Jafari S and Noiri T (2003). More on -semiopen sets. Note Mat. 22: 113-126.
• Caldas M, Jafari S and Saraf RK (2009). On a non-continuous and stronger form of Levine’s semi-continuous functions. Math. Commun. 14: 19-25.
• Janković DS (1983). On locally irreducible spaces. Ann. Soc. Sci. Bruxelles Sér. I 97: 59-72.
• Levine N (1963). Semi open sets and semi continuity in topological spaces. Amer. Math. Monthly 70: 36-41.
• Levine N (1970). Generalized closed sets in topology. Rend. Circ. Mat. Palermo (2) 19: 89-96.
• Mashhour AS, Abd El-Monsef ME and El-Deeb SN (1982). On precontinuous and weak precontinuous mappings. Proc. Math. Phys. Soc. Egypt 53: 47-53.
• Nasef AA and Noiri T (1998). Strong forms of faint continuity. Mem. Fac. Sci. Kochi Univ. Ser. A Math. 19: 21-28.
• Njåstad O (1965). On some classes of nearly open sets. Pacific J. Math. 15: 961-970.
• Noiri T (1996). Mildly normal spaces and some functions. Kyungpook Math. J. 36: 183-190.
• Palaniappan N and Rao KC (1993). Regular generalized closed sets. Kyungpook Math. J. 33: 211-219.
• Park JH, Lee BY and Son MJ (1997). On -semiopen sets in topological space. J. Indian Acad. Math. 19: 59-67.
• Rani IA and Balachandran K (1997). On regular generalized continuous maps in topological spaces. Kyungpook Math. J. 37: 305-314.
• Veličko NV (1968). H-closed topological spaces. Amer. Math. Soc. Transl. 78: 103-118.