Decompositions of g˘-Continuity in Topological Spaces
Keywords:
g˘-closed set, gα-closed set, gp-closed set, gt-set, ˘ gα⋆-set, ˘ gt-continuity and ˘ gα⋆-continuity
Abstract
The aim of this paper is to give decompositions of a weaker form of continuity, namely ˘ g-continuity, by providing the concepts of ˘ gt-sets, ˘ gα⋆-sets, ˘ gt-continuity and ˘ gα⋆-continuity.
References
P.Bhattacharya and B.K.Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382.
S.G.Crossley and S.K.Hildebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112.
J.Dontchev and M.Przemski, On the various decompositions of continuous and weakly continuous functions, Acta Math. Hungar.,71(1-2)(1996), 109-120.
M.Ganster and I.L.Reilly, A decomposition of continuity, Acta Math. Hungar., 56(1990), 299-301.
E.Hatir, T.Noiri and S.Yuksel, A decomposition of continuity, Acta Math. Hungar., 70(1-2)(1996), 145-150.
N.Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly, 68(1961), 44-46.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak pre continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53(1982), 47-53.
A.S.Mashhour, I.A.Hasanein and S.N.El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar., 41(1983), 213-218.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
T.Noiri, H.Maki and J.Umehara, Generalized preclosed functions, Mem. Fac. Sci. Kochi Univ. Math., 19(1998), 13-20.
T.Noiri, M.Rajamani and P.Sundaram, A decomposition of a weaker form of continuity, Acta Math. Hungar., 93(1- 2)(2001), 109-114.
M.Przemski, A decomposition of continuity and α-continuity, Acta Math. Hungar., 61(1991), 93-98.
O.Ravi and S.Ganesan, ¨ g-closed sets in topology, International Journal of computer science and emerging technologies, 2(3)(2011), 330-337.
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ g-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ gα-continuous functions in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ gα-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, On g˘p-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, On g˘p-continuous functions in topological spaces (submitted).
D.Rose, On Levine’s decomposition of continuity, Canad. Math. Bull., 21(1978), 477-481.
J.Tong, A decomposition of continuity, Acta Math. Hungar., 48(1986), 11-15.
J.Tong, On decomposition of continuity in topological spaces, Acta Math. Hungar., 54(1989), 51-55.
S.G.Crossley and S.K.Hildebrand, Semi-closure, Texas J. Sci., 22(1971), 99-112.
J.Dontchev and M.Przemski, On the various decompositions of continuous and weakly continuous functions, Acta Math. Hungar.,71(1-2)(1996), 109-120.
M.Ganster and I.L.Reilly, A decomposition of continuity, Acta Math. Hungar., 56(1990), 299-301.
E.Hatir, T.Noiri and S.Yuksel, A decomposition of continuity, Acta Math. Hungar., 70(1-2)(1996), 145-150.
N.Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly, 68(1961), 44-46.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak pre continuous mappings, Proc. Math. and Phys. Soc. Egypt, 53(1982), 47-53.
A.S.Mashhour, I.A.Hasanein and S.N.El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar., 41(1983), 213-218.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
T.Noiri, H.Maki and J.Umehara, Generalized preclosed functions, Mem. Fac. Sci. Kochi Univ. Math., 19(1998), 13-20.
T.Noiri, M.Rajamani and P.Sundaram, A decomposition of a weaker form of continuity, Acta Math. Hungar., 93(1- 2)(2001), 109-114.
M.Przemski, A decomposition of continuity and α-continuity, Acta Math. Hungar., 61(1991), 93-98.
O.Ravi and S.Ganesan, ¨ g-closed sets in topology, International Journal of computer science and emerging technologies, 2(3)(2011), 330-337.
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ g-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ gα-continuous functions in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, ˘ gα-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, On g˘p-closed sets in topological spaces (submitted).
O.Ravi, S.Padmasekaran, S.Usharani and I.Rajasekaran, On g˘p-continuous functions in topological spaces (submitted).
D.Rose, On Levine’s decomposition of continuity, Canad. Math. Bull., 21(1978), 477-481.
J.Tong, A decomposition of continuity, Acta Math. Hungar., 48(1986), 11-15.
J.Tong, On decomposition of continuity in topological spaces, Acta Math. Hungar., 54(1989), 51-55.
How to Cite
O.Ravi, S.Padmasekaran, & S.Usharani. (2015). Decompositions of g˘-Continuity in Topological Spaces. International Journal of Current Research in Science and Technology, 1(9), 1-6. Retrieved from https://crst.gfer.org/index.php/crst/article/view/40
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