Semi Generalized Open Sets and Generalized Semi Closed Sets in Topological Spaces

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Abdelgabar Adam Hassan, Semi Generalized Open Sets and Generalized Semi Closed Sets in Topological Spaces, Int. J. Anal. Appl., 18 (6) (2020), 1029-1036.

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Abdelgabar Adam Hassan

Abstract

In this paper we introduce a new class of semi generalized open sets, generalized semi closed sets in topological spaces, and studied some of its basic properties. Moreover we define approximately semi generalized open sets and approximately generalized semi closed sets in topological spaces. Further we obtained some properties of closure, semi generalized open sets and generalized semi closed sets in topological spaces.

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References

  1. J. Dugundji, Topology, Allyn and Bacon, Inc., Boston. 1966.
  2. S.A. Morris, Topology without tears, Unisia, 2001.
  3. S. Sekar, B. Jothilakshmi, On semi generalized star b - closed set in topological spaces, Int. J. Pure Appl. Math. 113 (2017), 93-102.
  4. S. Lipschutz, Schaum's outline of theory and problems of general topology, McGraw-Hill, New York. 1965.
  5. D. Lyappan, N. Nagaveni, On semi generalized b-continuous maps, semi generalized b-closed maps in topological space, Int. J. Math. Anal. 6 (2012), 1251-1264.
  6. S. S. Benchalli, P. G. Patil, P. M. Nalwad, Generalized ωα-Closed Sets in Topological Spaces, J. New Results Sci. 7 (2014), 7-19.
  7. N. Biswas, On Characterization of semi - continuous functions, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fsi. Mat. Natur. 48 (1970), 399-402.
  8. P. Bhattacharyya, B. K. Lahiri, Semi-generalized closed sets in topology, Ind. J. Math. 29 (1987), 375-382.
  9. N. Biswas, On characterizations of semi-continuous functions, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 8 (1970), 399-402.
  10. S.G. Crossly, S.K. Hildebrand, Semi- closure, Texas J. Sci. 22(1971), 99-112.
  11. S.G. Crossly, S.K. Hildebrand, Semi- topological properties, Fund. Math. 74 (1974), 233-254.
  12. S.P. Arya, T. Nour, Characterizations of S- normal spaces, Indian J. Pure. Appl. Math. 21 (8) (1990), 717-719.
  13. P. Bhattacharya, B. K. Lahiri, Semi- generalized closed sets in Topology, Indian J. Math. 29 (1987), 376-382.
  14. R. Devi, Studies on generalizations of closed maps and homeomorphisms in topological spaces, Ph.D. Thesis, Bharathiar University, Coimbatore (1994).
  15. N. Levine, On the commutivity of the closure and interior operator in topological spaces, Amer. Math. Mon. 68 (1961), 474-477.
  16. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Mon. 70 (1963), 36-41.
  17. N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (1970), 89-96.
  18. N. Biswas, On characterizations of semi- continuous functions, Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 399-402.
  19. S. S. Benchalli, P. G. Patil, T. D. Rayanagaudar, ωα-Closed Sets is Topological Spaces, Glob. J. Appl. Math. Math. Sci. 2 (2009), 53-63.
  20. D. Andrijivic Semi, pre-open sets, Mat, 1986, Vesnic, pp. 24-32.
  21. J. Weidmann, Spectral Theory of Ordinary Differential Operators, Springer-Verlag Berlin Heidelberg New York, 1987.
  22. P. Bhattacharya, B.K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29 (1987), 376-382.
  23. N. Levine, Generalized closed sets in topology, Rand. Circ. Mat. Palermo, 19 (1970), 89- 96.
  24. Y. Gnanambal, On Generalized Pre-Regular Closed Sets in Topological Spaces, Indian J. Pure Appl. Math. 28(1997), 351-360.