Skip to main content
SpringerLink
Log in

A unified theory for modifications ofg-closed sets

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

We introduce a new set calledmg-closed which is defined on a family of sets satisfying some minimal conditions. This set enables us to unify certain kind of modifications of generalized closed sets due to Levine [17].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abd El-Monsef M. E., El-Deeb S. N., Mahmoud R. A.,β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ.,12 (1983), 77–90.

    MathSciNet  Google Scholar 

  2. Andrijević D.,Semi-preopen sets, Mat. Vesnik,38 (1986), 24–32.

    MATH  MathSciNet  Google Scholar 

  3. Andrijević D.,On b-open sets, Mat. Vesnik,48 (1996), 59–64.

    MATH  MathSciNet  Google Scholar 

  4. Bhattacharyya P., Lahiri B. K.,Semi-generalized closed sets in topology, Indian J. Math.,29 (1987), 375–382.

    MATH  MathSciNet  Google Scholar 

  5. Caldas M., Ganster M., Georgiou D. N., Jafari S., Noiri T.,On ϱ-semiopen sets and separation axioms in topological spaces, (submitted).

  6. Caldas M., Georgiou D. N., Jafari S., Noiri T.,A unified theory of T 1/2-spaces, Annal. Univ. Sci. Budapest,45 (2003), 121–131.

    MathSciNet  Google Scholar 

  7. Crossley S. G., Hildebrand S. K.,Semi-closure, Texas J. Sci.,22 (1971), 99–112.

    Google Scholar 

  8. Császár A.,Generalized topology, generalized continuity, Acta Math. Hungar.,96 (2002), 351–357.

    Article  MATH  MathSciNet  Google Scholar 

  9. Dontchev J., Ganster M.,On δ-generalized closed sets and T 3/4-spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math.,17 (1996), 15–31.

    MATH  MathSciNet  Google Scholar 

  10. El-Deeb S. N., Hasanein I. A., Mashhour A. S., Noiri T.,On p-regular spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie,27(75) (1983), 311–315.

    MathSciNet  Google Scholar 

  11. Ganster M., Reilly I. L.,Locally closed sets and LC-continuous functions, Internat. J. Math. Math. Sci.,12 (1989), 417–424.

    Article  MATH  MathSciNet  Google Scholar 

  12. Granambal Y.,Studies on Generalized Pre-regular Closed Sets and Generalizations of Locally Closed Sets, Ph. D. Thesis, Bharathiar Univ., Coinbatore, 1998.

    Google Scholar 

  13. Granambal Y., Balachandran K.,β-locally closed sets and β-LC-continuous functions, Mem. Fac. Sci. Kochi Univ. Ser. A Math.,19 (1998), 35–44.

    MathSciNet  Google Scholar 

  14. Hatir E., Noiri T.,Decompositions of continuity and complete continuity, Acta Math. Hungar.,113 (2006), 281–287.

    Article  MATH  MathSciNet  Google Scholar 

  15. Khalimsky E. D., Kopperman R., Meyer P. R.,Computer graphics and connected topologies on finite ordered sets, Topology Appl.,36 (1990), 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  16. Levine N.,Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly,70 (1963), 36–41.

    Article  MATH  MathSciNet  Google Scholar 

  17. Levine N.,Generalized closed sets in topology, Rend. Circ. Mat. Palermo,19 (1970), 89–96.

    Article  MATH  MathSciNet  Google Scholar 

  18. Lugojan S.,Generalized topology, Stud. Cerc. Mat.,34 (1982), 348–360.

    MATH  MathSciNet  Google Scholar 

  19. Maki H., Devi R., Balachandran K.,Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. III,42 (1993), 13–21.

    MATH  Google Scholar 

  20. Maki H., Rao K. C., Nagoor A.,On generalizing semi-open and preopen sets, Pure Appl. Math. Sci.,49 (1999), 17–29.

    MathSciNet  Google Scholar 

  21. Mashhour A. S., Abd El-Monsef M. E., El-Deep S. N.,On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt,53 (1982), 47–53.

    MATH  MathSciNet  Google Scholar 

  22. Mashhour A. S., Allam A. A., Mahmoud F. S., Khedr F. H.,On surpratopological spaces, Indian J. Pure Appl. Math.,14 (1983), 502–510.

    MATH  MathSciNet  Google Scholar 

  23. Mashhour A. S., Hasanein I. A., El-Deeb S. N.,α-continuous and α-open mappings, Acta Math. Hungar.,41 (1983), 213–218.

    Article  MATH  MathSciNet  Google Scholar 

  24. Njåstad O.On some classes of nearly open sets, Pacific J. Math.,15 (1965), 961–970.

    MATH  MathSciNet  Google Scholar 

  25. Noiri T., Maki H., Umehara J.,Generalized preclosed functions, Mem. Fac. Sci. Kochi Univ. Ser. A Math.,19 (1998), 13–20.

    MATH  MathSciNet  Google Scholar 

  26. Noiri T., Popa V.,On m-almost continuous multifunctions, Istanbul J. Math. Phys. Astro. Fac. Sci. (N. S.),1 (2004/2005), (to appear).

  27. Park J. H., Lee B. Y., Son M. J.,On δ-semiopen sets in topological spaces, J. Indian Acad. Math.,19 (1997), 59–67.

    MATH  MathSciNet  Google Scholar 

  28. Popa V., Noiri T.,On M-continuous functions, Anal. Univ. “Dunârea de Jos” Galaţi, Ser. Mat. Fiz. Mec. Teor. (2),18(23) (2000), 31–41.

    Google Scholar 

  29. Popa V., Noiri T.,A unified theory of weak continuity for functions, Rend. Circ. Mat. Palermo,51 (2002), 439–464.

    Article  MATH  MathSciNet  Google Scholar 

  30. Raychaudhuri S., Mukherjee M. N.,On δ-almost continuity and δ-preopen sets, Bull. Inst. Math. Acad. Sinica,21 (1993), 357–366.

    MATH  MathSciNet  Google Scholar 

  31. Sundaram P., Balachandran K.,Semi generalized locally closed sets in topological spaces, (preprint).

  32. Veličko N. V.,H-closed topological spaces, Amer. Math. Soc. Transl. (2),78 (1968), 103–118.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 2949-1 Shiokita-cho, Hinagu, Yatsushiro-shi, 869-5142, Kumamoto-ken, Japan

    Takashi Noiri

Authors
  1. Takashi Noiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noiri, T. A unified theory for modifications ofg-closed sets. Rend. Circ. Mat. Palermo 56, 171–184 (2007). https://doi.org/10.1007/BF03031437

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03031437

Mathematics Subject Classification (2000)

Keys words and phrases

Search

Navigation