On (1, 2)⋆-g⋆-continuous functions
Keywords:
(1, 2)⋆-T1/2-space, (1, 2)⋆-α-space, (1, 2)⋆-αg-irresolute function, (1, 2)⋆-g⋆-continuous function, (1, 2)⋆-gα⋆ -continuous function, (1, 2)⋆-gsp-continuous function
Abstract
The aim of this paper is to study (1, 2)⋆-g⋆-continuous functions in bitopological spaces and investigate their relations with various generalized (1, 2)⋆-continuous functions. We also discuss some properties of (1, 2)⋆-g⋆-continuous functions. We also introduce (1, 2)⋆-g⋆-irresolute functions and study some of its applications. Finally using (1, 2)⋆-g⋆-continuous functions we obtain a decomposition of (1, 2)⋆-continuity.
References
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F.G.Arenas, J.Dontchev and M.Ganster, On λ-sets and dual of generalized continuity, Questions Answers Gen. Topology, 15 (1997), 3-13.
S.P.Arya and T.M.Nour, Characterizations of s-normal spaces, Indian J. Pure. Appl. Math., 21(8)(1990), 717-719.
K.Balachandran, P.Sundaram and H.Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. Math., 12(1991), 5-13.
P.Bhattacharyya and B.K.Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382. [8] D.E.Cameron, Topology atlas, http://gozips. uakron. deu/.
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J.Cao, M.Ganster and I.Reilly, Submaximality, extremal disconnectedness and generalized closed sets, Houston J. Math., 24(1998), 681-688.
R.Devi, K.Bhuvaneswari and H.Maki, Weak forms of gρ-closed sets, where ρ ∈ { α, α⋆, α⋆⋆} and digital plane, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 25(2004), 37-54.
R.Devi, K.Balachandran and H.Maki, On generalized α-continuous maps and α-generalized continuous maps, Far East J. Math. Sci., Special Volume, Part I(1997), 1-15.
J.Dontchev and M.Ganster, On δ-generalized closed sets and T3/4-spaces, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 17 (1996), 15-31.
W.Dunham, T1/2-spaces, Kyungpook Math. J., 17(1977), 161-169.
Z.Duszynski, M.Jeyaraman, M.S.Joseph, O.Ravi and M.L.Thivagar, A new generalization of closed sets in bitopology, South Asian Journal of Mathematics, 4(5)(2014), 215-224.
K.Kayathri, O.Ravi, M.L.Thivagar and M.Joseph Israel, Decompositions of (1, 2)⋆-rg-continuous maps in bitopological spaces, Antarctica J. Math., 6(1)(2009), 13-23.
J.C.Kelly, Bitopological spaces, Proc. London Math. Soc., 13(1963), 71-89.
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N.Levine, Some remarks on the closure operator in topological spaces, Amer. Math. Monthly, 70(5)(1963), 553.
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O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
M.Rajamani and K.Viswanathan, On αgs-closed sets in topological spaces, Acta Ciencia Indica, XXXM(3)(2004), 21-25.
C.Rajan, Further study of new bitopological generalized continuous functions, Ph. D Thesis, Madurai Kamaraj University, Madurai, (2014).
O.Ravi, M.L.Thivagar and E.Hatir, Decomposition of (1, 2)⋆-continuity and (1, 2)⋆-α-continuity, Miskolc Mathematical Notes., 10(2)(2009), 163-171.
O.Ravi and M.L.Thivagar, Remarks on λ-irresolute functions via (1, 2)⋆-sets, Advances in App. Math. Analysis, 5(1) (2010), 1-15.
O.Ravi, M.Jeyaraman, M.Sajan Joseph and R.Muthuraj, (1, 2)⋆-g⋆-closed sets, submitted.
O.Ravi, E.Ekici and M.Lellis Thivagar, On (1, 2)⋆-sets and decompositions of bitopological (1, 2)⋆-continuous mappings, Kochi J. Math., 3(2008), 181-189.
O.Ravi, K.Kayathri, M.L.Thivagar and M.Joseph Israel, Mildly (1, 2)⋆-normal spaces and some bitopological functions, Mathematica Bohemica, 135(1)(2010), 1-15.
O.Ravi, A.Pandi and R.Latha, Contra-pre-(1, 2)⋆-semi-continuous functions, Bessel Journal of Mathematics (To appear).
O.Ravi, S.Pious Missier and T.Salai Parkunan, On bitopological (1, 2)⋆-generalized homeomorphisms, Int J. Contemp. Math. Sciences., 5(11)(2010),
O.Ravi, M.L.Thivagar and E.Ekici, Decomposition of (1, 2)⋆-continuity and complete (1, 2)⋆-continuity in bitopological spaces, Analele Universitatii Din Oradea. Fasc. Matematica Tom XV (2008), 29-37.
O.Ravi, M.L.Thivagar and Jinjinli, Remarks on extensions of (1, 2)⋆-g-closed maps, Archimedes J. Math., 1(2)(2011), 177-187.
O.Ravi, A.Pandi, S.Pious Missier and T.Salai Parkunan, Remarks on bitopological (1, 2)⋆-rω-Homeomorphisms, International Journal of Mathematical Archive, 2(4)(2011), 465-475.
M.Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph.D Thesis, Bharathiar University, Coimbatore, September, (2002).
M.K.R.S.Veera Kumar, g#-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. (Math.)., 24(2003), 1-13.
M.K.R.S.Veera Kumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 21(2000), 1-19.
M.K.R.S.Veera Kumar, ˆ g-closed sets in topological spaces, Bull. Allah. Math. Soc., 18(2003), 99-112.543-557.
D.Andrijevic, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
J.Antony Rex Rodrigo, O.Ravi, A.Pandi and C.M.Santhana, On (1, 2)⋆-s-normal spaces and pre-(1, 2)⋆-gs-closed functions, International Journal of Algorithms, Computing and Mathematics, 4(1)(2011), 29-42.
F.G.Arenas, J.Dontchev and M.Ganster, On λ-sets and dual of generalized continuity, Questions Answers Gen. Topology, 15 (1997), 3-13.
S.P.Arya and T.M.Nour, Characterizations of s-normal spaces, Indian J. Pure. Appl. Math., 21(8)(1990), 717-719.
K.Balachandran, P.Sundaram and H.Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. Math., 12(1991), 5-13.
P.Bhattacharyya and B.K.Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29(3)(1987), 375-382. [8] D.E.Cameron, Topology atlas, http://gozips. uakron. deu/.
J.Cao, M.Ganster and I.Reilly, On sg-closed sets and gα-closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 20(1999), 1-5.
J.Cao, M.Ganster and I.Reilly, Submaximality, extremal disconnectedness and generalized closed sets, Houston J. Math., 24(1998), 681-688.
R.Devi, K.Bhuvaneswari and H.Maki, Weak forms of gρ-closed sets, where ρ ∈ { α, α⋆, α⋆⋆} and digital plane, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 25(2004), 37-54.
R.Devi, K.Balachandran and H.Maki, On generalized α-continuous maps and α-generalized continuous maps, Far East J. Math. Sci., Special Volume, Part I(1997), 1-15.
J.Dontchev and M.Ganster, On δ-generalized closed sets and T3/4-spaces, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 17 (1996), 15-31.
W.Dunham, T1/2-spaces, Kyungpook Math. J., 17(1977), 161-169.
Z.Duszynski, M.Jeyaraman, M.S.Joseph, O.Ravi and M.L.Thivagar, A new generalization of closed sets in bitopology, South Asian Journal of Mathematics, 4(5)(2014), 215-224.
K.Kayathri, O.Ravi, M.L.Thivagar and M.Joseph Israel, Decompositions of (1, 2)⋆-rg-continuous maps in bitopological spaces, Antarctica J. Math., 6(1)(2009), 13-23.
J.C.Kelly, Bitopological spaces, Proc. London Math. Soc., 13(1963), 71-89.
M.Lellis Thivagar, O.Ravi and M.E.Abd El-Monsef, Remarks on bitopological (1, 2)⋆-quotient mappings, J. Egypt Math. Soc., 16(1)(2008), 17-25.
N.Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo, 19(2)(1970), 89-96.
N.Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
N.Levine, Some remarks on the closure operator in topological spaces, Amer. Math. Monthly, 70(5)(1963), 553.
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.
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(1965), 961-970.
M.Rajamani and K.Viswanathan, On αgs-closed sets in topological spaces, Acta Ciencia Indica, XXXM(3)(2004), 21-25.
C.Rajan, Further study of new bitopological generalized continuous functions, Ph. D Thesis, Madurai Kamaraj University, Madurai, (2014).
O.Ravi, M.L.Thivagar and E.Hatir, Decomposition of (1, 2)⋆-continuity and (1, 2)⋆-α-continuity, Miskolc Mathematical Notes., 10(2)(2009), 163-171.
O.Ravi and M.L.Thivagar, Remarks on λ-irresolute functions via (1, 2)⋆-sets, Advances in App. Math. Analysis, 5(1) (2010), 1-15.
O.Ravi, M.Jeyaraman, M.Sajan Joseph and R.Muthuraj, (1, 2)⋆-g⋆-closed sets, submitted.
O.Ravi, E.Ekici and M.Lellis Thivagar, On (1, 2)⋆-sets and decompositions of bitopological (1, 2)⋆-continuous mappings, Kochi J. Math., 3(2008), 181-189.
O.Ravi, K.Kayathri, M.L.Thivagar and M.Joseph Israel, Mildly (1, 2)⋆-normal spaces and some bitopological functions, Mathematica Bohemica, 135(1)(2010), 1-15.
O.Ravi, A.Pandi and R.Latha, Contra-pre-(1, 2)⋆-semi-continuous functions, Bessel Journal of Mathematics (To appear).
O.Ravi, S.Pious Missier and T.Salai Parkunan, On bitopological (1, 2)⋆-generalized homeomorphisms, Int J. Contemp. Math. Sciences., 5(11)(2010),
O.Ravi, M.L.Thivagar and E.Ekici, Decomposition of (1, 2)⋆-continuity and complete (1, 2)⋆-continuity in bitopological spaces, Analele Universitatii Din Oradea. Fasc. Matematica Tom XV (2008), 29-37.
O.Ravi, M.L.Thivagar and Jinjinli, Remarks on extensions of (1, 2)⋆-g-closed maps, Archimedes J. Math., 1(2)(2011), 177-187.
O.Ravi, A.Pandi, S.Pious Missier and T.Salai Parkunan, Remarks on bitopological (1, 2)⋆-rω-Homeomorphisms, International Journal of Mathematical Archive, 2(4)(2011), 465-475.
M.Sheik John, A study on generalizations of closed sets and continuous maps in topological and bitopological spaces, Ph.D Thesis, Bharathiar University, Coimbatore, September, (2002).
M.K.R.S.Veera Kumar, g#-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. (Math.)., 24(2003), 1-13.
M.K.R.S.Veera Kumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 21(2000), 1-19.
M.K.R.S.Veera Kumar, ˆ g-closed sets in topological spaces, Bull. Allah. Math. Soc., 18(2003), 99-112.543-557.
How to Cite
O. Ravi, M. Jeyaraman, M. Sajan Joseph, & R. Muthuraj. (2015). On (1, 2)⋆-g⋆-continuous functions. International Journal of Current Research in Science and Technology, 1(8), 1-11. Retrieved from https://crst.gfer.org/index.php/crst/article/view/36
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