New topological approach of generalized closed sets

Yıl 2015, Cilt: 4 Sayı: 9, 67 - 78, 01.09.2015

Arafa Nasef Roshdey Mareay

Öz

Closedness is a basic concept for the study and the investigation in the general topological spaces. (Fukutake, Nasef and El- Maghrabi, 2003) introduced a new weakly form of generalized closed sets,γg−closed set, which is weaker than both of gs−closed sets (Arya and Nour, 1990), gp−closed sets (Noiri, Maki and Umehara, 1998) and stronger than gsp−closed sets (Dontchev,1995). In this paper, we introduce more study of γg−closed sets in a general topological space

Anahtar Kelimeler

γ−closed set, γg−closed set

Kaynakça

• Z. Pawlak, Rough sets: theortical aspects of reasoning about data Systems theory, Knowledge engineering and problem solving, 9, Dordrecht; Kluwer, 1991.
• S.G. Crossley, S.K. Hildebrand, Semi-topological properties, Fund. Math., 74, 233- 254, 1972.
• A.S. Davis, Indexed systems of neighborhood for general topological spaces, Amer. Math. Monthy, 68, 886-893, 1961.
• D.S. Jankovi`c, On some seperation axioms and θ-closure, Math. Vesnik, 32(4), 439-449, 1980.
• T. Noiri, On δ-continuous functions, J. Korean Mtah. Soc., 16, 161-166, 1980.
• O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15, 961-970, 1965.
• N. Levine, Semi-open sets and semi-continuty in topological spaces, Amer. Math. Monthly, 70, 36-41, 1963.
• A.S. Mashhour, M.E. Abd El-Mosef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53, 47-53, 1982.
• A.A. El-Atik, A study of some types of mappings on topological spaces, M.Sc. Thesis, Tanta Univ., Egypt,(1997).
• J. Dontchev, M. Przenski, On the various decopositions of continuous and some weakly continuous functions, Acta Math. Hungar., 71(1-2), 109-120, 1996.
• D. Andrijevi´c, Semi-preopen sets, Mat. Vesnik, 38, 24-32, 1986.
• M.E. Abd. E1-Monsef, S.N. El-Deeb, R.A. Mahmoud, β-open sets and β-continous mappings, Bull. Fac. Sci. Assiut Univ., 12, 77-90, 1983.
• J. Cao, S. Greenwood, I. Reilly, Generalized closed sets: a unified approach, Applied General Topology, 2, 179-189, 2001.
• T. Fukutake, A.A. Nasef, A.I. El-Maghrabi, Some topological concepts via γ−gneralized closed sets, Bull. of Fukuoka University of Edu., 52, Part III, 1-9, 2003.
• N. Levine, Generalized closed sets in topology, Rend Circ Mat Palermo, 19(1970), 89-96.
• S.P. Arya, T. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math., 21, 717-719, 1990.
• J. Dontechev , On generalizing semi-preclosed sets, Mem. Fac. Sci. Kochi Univ. (Math.), 16, 35-48, 1995.
• H. Maki, R. Devi and K. Balachandran, Associated topologies of generlaized α- closed sets, Mem. Fac. Sci. Kochi. Univ. (Math.), 15,51-63, 1994.
• T. Noiri, H. Maki, J. Umehara, Generalized preclosed function, Mem. Fac. Sci. Kochi. Univ. (Math), 19, 13-20, 1998.
• P. Bhattacharyga, B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math., 29, 375-382, 1987.
• H. Maki, R. Devi, K. Balachandran, generalized α- closed sets in topology, Bull. Eukuoka Univ Ed. part III, 42, 13-21, 1993.
• D.S. Jankovi`c, A note on mappings of extremally discoonected spaces, Acta Math. Hung., 46(1-2), 83-92, 1985.
• J. Cao, M. Ganster, I. Reilly, Submaximality, extremal disconnectedness and generalized closed sets, Huston J. Math., 24, 681-688, 1981.
• H. Maki, K. Balachandran, R. Devi, Remarks on semi-generalized closed sets and generalized semi-closed sets, Kyungpook Math. J., 36, 155- 163, 1996.
• D. Jankovi´c, I. Reilly, On semi-sepration properties, Indian J. Pure Appl. Math., 16, 957-964, 1985.
• J. Dontechev, H. Maki, On the behaviour of gp−closed sets and their generalizations, Mem. Fac. Sci. Kochi Univ. (Math.), 19, 57-72, 1998.
• J. Dontechev , On some seperation axioms associated with the α−topology, Mem. Fac. Sci. Kochi Univ. (Math.), 18, 31-35, 1997.
• M. Ganster, M. Steiner, On some questions about b−open sets, Q and A in general Topology, 25(1), 83-86, 2007.
• D. Andrijevi´c, On b-open sets, Mat. Vesnik, 48, 64-69, 1996.
• J. Dontchev, H. Maki, On sg-closed sets and semi-λ-closed sets, Questions Answers Gen. Topology, 15, 259-266, 1997.
• J. Cao, M. Ganster, I. Reilly, On generalized closed sets, Topology Appl. Proceedings of the 1998 Gyula Topology Colloquium, to appear.
• E.D. Khalimsky, R. Kopperman, P.R. Meyer, Computer graphics and connected toplogies on finite ordered sets, Topol. Appl., 30, 1-17, 1990.
• T.Y. Kong, R. Kopperman, P.R. Meyer, A topological approach to digital topology, Am. Math. Month, 98, 901-917, 1991.
• M.S. El Naschie, On the uncertainty of cantorian geometry and two-slit experiment, Chaos, Soliton and Fractals, 9(3), 517-529, 1998.