New topological approach of generalized closed sets

Volume: 4 Number: 9 September 1, 2015
Arafa Nasef , Roshdey Mareay
EN

New topological approach of generalized closed sets

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

Keywords

γ−closed set, γg−closed set

References

  1. Z. Pawlak, Rough sets: theortical aspects of reasoning about data Systems theory, Knowledge engineering and problem solving, 9, Dordrecht; Kluwer, 1991.
  2. S.G. Crossley, S.K. Hildebrand, Semi-topological properties, Fund. Math., 74, 233- 254, 1972.
  3. A.S. Davis, Indexed systems of neighborhood for general topological spaces, Amer. Math. Monthy, 68, 886-893, 1961.
  4. D.S. Jankovi`c, On some seperation axioms and θ-closure, Math. Vesnik, 32(4), 439-449, 1980.
  5. T. Noiri, On δ-continuous functions, J. Korean Mtah. Soc., 16, 161-166, 1980.
  6. O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15, 961-970, 1965.
  7. N. Levine, Semi-open sets and semi-continuty in topological spaces, Amer. Math. Monthly, 70, 36-41, 1963.
  8. 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.
  9. A.A. El-Atik, A study of some types of mappings on topological spaces, M.Sc. Thesis, Tanta Univ., Egypt,(1997).
  10. J. Dontchev, M. Przenski, On the various decopositions of continuous and some weakly continuous functions, Acta Math. Hungar., 71(1-2), 109-120, 1996.
APA
Nasef, A., & Mareay, R. (2015). New topological approach of generalized closed sets. Journal of New Results in Science, 4(9), 67-78. https://izlik.org/JA35JM59BC
AMA
1.Nasef A, Mareay R. New topological approach of generalized closed sets. JNRS. 2015;4(9):67-78. https://izlik.org/JA35JM59BC
Chicago
Nasef, Arafa, and Roshdey Mareay. 2015. “New Topological Approach of Generalized Closed Sets”. Journal of New Results in Science 4 (9): 67-78. https://izlik.org/JA35JM59BC.
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
[1]A. Nasef and R. Mareay, “New topological approach of generalized closed sets”, JNRS, vol. 4, no. 9, pp. 67–78, Sept. 2015, [Online]. Available: https://izlik.org/JA35JM59BC
ISNAD
Nasef, Arafa - Mareay, Roshdey. “New Topological Approach of Generalized Closed Sets”. Journal of New Results in Science 4/9 (September 1, 2015): 67-78. https://izlik.org/JA35JM59BC.
JAMA
1.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, Sept. 2015, pp. 67-78, https://izlik.org/JA35JM59BC.
Vancouver
1.Arafa Nasef, Roshdey Mareay. New topological approach of generalized closed sets. JNRS [Internet]. 2015 Sep. 1;4(9):67-78. Available from: https://izlik.org/JA35JM59BC