On Contra $\pi g\gamma$-Continuous Functions
DOI:
https://doi.org/10.26713/jims.v6i2.258Keywords:
$\pi g\gamma$-closed set, $\pi g\gamma$-continuous function, contra $\pi g\gamma$-continuous function, contra $\pi g\gamma$-graph, $\pi g\gamma$-normal spaceAbstract
In this paper, we introduce and investigate the notion of contra $\pi g\gamma$-continuous functions by utilizing $\pi g\gamma$-closed sets [31]. We obtain fundamental properties of contra $\pi g\gamma$-continuous functions and discuss the relationships between contra $\pi g\gamma$-continuity and other related functions.Downloads
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M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, $beta$-open sets and $beta$-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12(1983), 77-90.
M. Akdag and A. Ozkan, Some properties of contra $gb$-continuous functions, Journal of New Results in Science 1(2012), 40-49.
S.C. Akgun and G. Aslim, On $pi gb$-closed sets and related topics, International Journal of Mathematical Archive 3(5)(2012), 1873-1884.
D. Andrijevic, On $b$-open sets, Mat. Vesnik 48(1-2)(1996), 59-64.
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, S. Jafari, K. Viswanathan and S. Krishnaprakash, On contra $gamma gp$-continuous functions, Kochi J. Math. 5(2010), 67-78.
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 $gamma g$-closed sets, Acta Math. Hungar. 89(3)(2000), 211-219.
J. Dontchev and M. Przemski, On the various decompositions of continuous and some weakly continuous functions, Acta Math. Hungar. 71(1-2)(1996), 109-120.
E. Ekici, On $gamma$-normal spaces, Bull. Math. Soc. Sci. Math. Roumanie (N.S) 50(98)(2007), 259-272.
E. Ekici and C.W. Baker, On $gamma g$-closed sets and continuity, Kochi J. Math. 2(2007), 35-42.
E. Ekici, On $(g,s)$-continuous and $(gamma g,s)$-continuous functions, Sarajevo J. Math. 3(15)(2007), 99-113.
E. Ekici, On contra $gamma g$-continuous functions, Chaos Solitons and Fractals 35(2008), 71-81.
A.A. El-Atik, A study on some types of mappings on topological spaces, Master's Thesis, Tanta University, Egypt, 1997.
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, $gamma$-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.
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 $R_0$ and pairwise $R_1$ bitopological spaces, Bull. Math. Soc. Sci. Math. RS Roumanie. (N.S) 30(78)(1986), 141-148.
A.A. Nasef, Some properties of contra-$gamma$-continuous functions, Chaos Solitons and Fractals 24(2)(2005), 471-477.
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 $gamma gp$-closed sets in topological spaces, Indian J. Pure Appl. Math. (in press).
O. Ravi, S. Margaret Parimalam, S. Murugesan and A. Pandi, Slightly $gamma g$-continuous functions, Journal of New Results in Science, 3(2013), 60-71.
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.
D. Sreeja and C. Janaki, On $gamma gb$-closed sets in topological spaces, International Journal of Mathematical Archive 2(8)(2011), 1314-1320.
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. 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.
V. Zaitsev, On certain classes of topological spaces and their bicompactifications, Dokl. Akad. Nauk. SSSR 178(1968), 778-779.
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