On Contra gβ-Continuous Functions
Keywords:
gβ-closed set, gβ-continuous function, contra gβ-continuous function, contra gβ-graph, gβ-normal space
Abstract
In this paper, we introduce and investigate the notion of contra gβ-continuous functions by utilizing gβ-closed sets [33]. We obtain fundamental properties of contra gβ-continuous functions and discuss the relationships between contra gβ- continuity and other related functions.
References
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S.P.Arya and R.Gupta, On strongly continuous mappings, Kyungpook Math. J., 14(1974), 131-143.
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M.Caldas, S.Jafari, T.Noiri and M.Simoes, A new generalization of contra-continuity via Levine’s g-closed sets, Chaos Solitons and Fractals, 32(2007), 1597-1603.
M.Caldas and S.Jafari, Some properties of contra-β-continuous functions, Mem. Fac. Sci. Kochi Univ. (Math.)., 22(2001), 19-28.
M.Caldas and S.Jafari, On rarely gβ-continuous functions, An. Stiint. Univ. Al. I. Cuza Iasi, Ser. Noua, Mat., 60(2005), 337-344.
M.Caldas, S.Jafari, K.Viswanathan and S.Krishnaprakash, On contra πgp-continuous functions, Kochi J. Math., 5(2010), 67-78.
R.Devi, K.Balachandran and H.Maki, Semi-generalized closed maps and generalized semi-closed maps, Mem. Fac. Kochi Univ. Ser. A. Math., 14(1993), 41-54.
J.Dontchev, Contra-continuous functions and strongly S-closed spaces, Internat. J. Math. and Math. Sci., 19(1996), 303-310.
J.Dontchev and T.Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar., 89(3)(2000), 211-219.
E.Ekici and C.W.Baker, On πg-closed sets and continuity, Kochi J. Math., 2(2007), 35-42.
E.Ekici, On (g, s)-continuous and (πg, s)-continuous functions, Sarajevo J. Math., 3(15)(2007), 99-113.
E.Ekici, On contra πg-continuous functions, Chaos Solitons and Fractals, 35(2008), 71-81.
M.Ganster and D.Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math. Compu. Sci. Math., 1(1988), 65-75.
S.Jafari and T.Noiri, On contra precontinuous functions, Bull. Malaysian Math. Sci. Soc., 25(2002), 115-128.
S.Jafari and T.Noiri, Contra-super-continuous functions, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 42(1999), 27-34.
L.N.Kalantan, π-normal topological spaces, Filomat., 22(1)(2008), 173-181.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
N.Levine, On the commutivity of the closure and interior operator in the topological spaces, Amer. Math. Monthly, 68(1961), 474-477.
A.S.Mashour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt., 53(1982), 47-53.
M.Mrsevic, On pairwise R0 and pairwise R1 bitopological spaces, Bull. Math. Soc. Sci. Math RS Roumanie. (N.S) 30(78)(2)(1986), 141-148.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
T.Noiri, Super-continuity and some strong forms of continuity, Indian J. Pure Appl. Math., 15(1984), 241-250.
T.Noiri, Characterizations of extremally disconnected spaces, Indian J. Pure Appl. Math., 19(4)(1988), 325-329.
T.Noiri, H.Maki and J.Umehara, Generalized preclosed functions, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 19(1998), 13-20.
J.H.Park, M.J.Son and B.Y.Lee, On πgp-closed sets in topological spaces, Indian J. Pure Appl. Math., (In press).
O.Ravi, S.Margaret Parimalam, A.Pandi and S.Murugesan, On contra πgβ-continuous functions, Submitted.
T.Soundararajan, Weakly Hausdroff spaces and the cardinality of topological spaces, 1971 General Topology and its Relation to Modern Analysis and Algebra. III, (Proc. Conf. Kanpur, 1968). Academia. Prague 1971, 301-306.
R.Staum, The algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169-185.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
S.Tahiliani, On πgβ-closed sets in topological spaces, Note Di Mat., 30(1)(2010), 49-55.
S.Takigawa and H.Maki, Every nonempty open set of the digital n-space is expressible as the union of finitely many nonempty regular open sets, Sci. Math. Jpn., 67(2008), 365-376.
K.V.Tamil Selvi, P.Thangaraj and O.Ravi, On contra gγ-continuous functions, Submitted.
V.Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR, 178(1968), 778-779.
S.P.Arya and R.Gupta, On strongly continuous mappings, Kyungpook Math. J., 14(1974), 131-143.
N.Bourbaki, General topology, Part I, Reading, Ma: Addison wesley, Paris, (1966).
M.Caldas, S.Jafari, T.Noiri and M.Simoes, A new generalization of contra-continuity via Levine’s g-closed sets, Chaos Solitons and Fractals, 32(2007), 1597-1603.
M.Caldas and S.Jafari, Some properties of contra-β-continuous functions, Mem. Fac. Sci. Kochi Univ. (Math.)., 22(2001), 19-28.
M.Caldas and S.Jafari, On rarely gβ-continuous functions, An. Stiint. Univ. Al. I. Cuza Iasi, Ser. Noua, Mat., 60(2005), 337-344.
M.Caldas, S.Jafari, K.Viswanathan and S.Krishnaprakash, On contra πgp-continuous functions, Kochi J. Math., 5(2010), 67-78.
R.Devi, K.Balachandran and H.Maki, Semi-generalized closed maps and generalized semi-closed maps, Mem. Fac. Kochi Univ. Ser. A. Math., 14(1993), 41-54.
J.Dontchev, Contra-continuous functions and strongly S-closed spaces, Internat. J. Math. and Math. Sci., 19(1996), 303-310.
J.Dontchev and T.Noiri, Quasi-normal spaces and πg-closed sets, Acta Math. Hungar., 89(3)(2000), 211-219.
E.Ekici and C.W.Baker, On πg-closed sets and continuity, Kochi J. Math., 2(2007), 35-42.
E.Ekici, On (g, s)-continuous and (πg, s)-continuous functions, Sarajevo J. Math., 3(15)(2007), 99-113.
E.Ekici, On contra πg-continuous functions, Chaos Solitons and Fractals, 35(2008), 71-81.
M.Ganster and D.Andrijevic, On some questions concerning semi-preopen sets, J. Inst. Math. Compu. Sci. Math., 1(1988), 65-75.
S.Jafari and T.Noiri, On contra precontinuous functions, Bull. Malaysian Math. Sci. Soc., 25(2002), 115-128.
S.Jafari and T.Noiri, Contra-super-continuous functions, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 42(1999), 27-34.
L.N.Kalantan, π-normal topological spaces, Filomat., 22(1)(2008), 173-181.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
N.Levine, On the commutivity of the closure and interior operator in the topological spaces, Amer. Math. Monthly, 68(1961), 474-477.
A.S.Mashour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt., 53(1982), 47-53.
M.Mrsevic, On pairwise R0 and pairwise R1 bitopological spaces, Bull. Math. Soc. Sci. Math RS Roumanie. (N.S) 30(78)(2)(1986), 141-148.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
T.Noiri, Super-continuity and some strong forms of continuity, Indian J. Pure Appl. Math., 15(1984), 241-250.
T.Noiri, Characterizations of extremally disconnected spaces, Indian J. Pure Appl. Math., 19(4)(1988), 325-329.
T.Noiri, H.Maki and J.Umehara, Generalized preclosed functions, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 19(1998), 13-20.
J.H.Park, M.J.Son and B.Y.Lee, On πgp-closed sets in topological spaces, Indian J. Pure Appl. Math., (In press).
O.Ravi, S.Margaret Parimalam, A.Pandi and S.Murugesan, On contra πgβ-continuous functions, Submitted.
T.Soundararajan, Weakly Hausdroff spaces and the cardinality of topological spaces, 1971 General Topology and its Relation to Modern Analysis and Algebra. III, (Proc. Conf. Kanpur, 1968). Academia. Prague 1971, 301-306.
R.Staum, The algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math., 50(1974), 169-185.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
S.Tahiliani, On πgβ-closed sets in topological spaces, Note Di Mat., 30(1)(2010), 49-55.
S.Takigawa and H.Maki, Every nonempty open set of the digital n-space is expressible as the union of finitely many nonempty regular open sets, Sci. Math. Jpn., 67(2008), 365-376.
K.V.Tamil Selvi, P.Thangaraj and O.Ravi, On contra gγ-continuous functions, Submitted.
V.Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR, 178(1968), 778-779.
How to Cite
K.Amutha, K.M.Dharmalingam, & O.Ravi. (2017). On Contra gβ-Continuous Functions. International Journal of Current Research in Science and Technology, 3(2), 1-11. Retrieved from https://crst.gfer.org/index.php/crst/article/view/82
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