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New topological approach of generalized closed sets

Year 2015, Volume: 4 Issue: 9, 67 - 78, 01.09.2015

Abstract

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

References

  • 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.
Year 2015, Volume: 4 Issue: 9, 67 - 78, 01.09.2015

Abstract

References

  • 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.
There are 34 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Arafa Nasef

Roshdey Mareay This is me

Publication Date September 1, 2015
Published in Issue Year 2015 Volume: 4 Issue: 9

Cite

APA Nasef, A., & Mareay, R. (2015). New topological approach of generalized closed sets. Journal of New Results in Science, 4(9), 67-78.
AMA Nasef A, Mareay R. New topological approach of generalized closed sets. JNRS. September 2015;4(9):67-78.
Chicago Nasef, Arafa, and Roshdey Mareay. “New Topological Approach of Generalized Closed Sets”. Journal of New Results in Science 4, no. 9 (September 2015): 67-78.
EndNote Nasef A, Mareay R (September 1, 2015) New topological approach of generalized closed sets. Journal of New Results in Science 4 9 67–78.
IEEE A. Nasef and R. Mareay, “New topological approach of generalized closed sets”, JNRS, vol. 4, no. 9, pp. 67–78, 2015.
ISNAD Nasef, Arafa - Mareay, Roshdey. “New Topological Approach of Generalized Closed Sets”. Journal of New Results in Science 4/9 (September 2015), 67-78.
JAMA Nasef A, Mareay R. New topological approach of generalized closed sets. JNRS. 2015;4:67–78.
MLA Nasef, Arafa and Roshdey Mareay. “New Topological Approach of Generalized Closed Sets”. Journal of New Results in Science, vol. 4, no. 9, 2015, pp. 67-78.
Vancouver Nasef A, Mareay R. New topological approach of generalized closed sets. JNRS. 2015;4(9):67-78.


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