Skip to main content
SpringerLink
Log in

A unified theory of R-continuity

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We introduce and investigate R-M-continuous functions defined between sets satisfying some minimal conditions. The functions enable us to formulate a unified theory of modifications of R-continuity [22]: R-irresoluteness [6], R-preirresoluteness [7].

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

    MathSciNet  Google Scholar 

  2. M. E. Abd El-Monsef, R. A. Mahmoud and E. R. Lashin, β-closure and β-interior, J. Fac. Ed. Ain Shams Univ., 10 (1986), 235–245.

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  5. C. W. Baker, Contra-open functions and contra-closed functions, Math. Today (Ahmedabad), 15 (1997), 19–24.

    MATH  MathSciNet  Google Scholar 

  6. C. W. Baker, R-irresolute functions, Acta Cienica Indica, 30 (2004), 775–780.

    Google Scholar 

  7. C. W. Baker, R-preirresolute functions, Carpathian J. Math., 21 (2005), 1–6.

    MATH  MathSciNet  Google Scholar 

  8. M. Caldas, S. Jafari and T. Noiri, Charactrizations of pre-R 0 and pre-R 1 topological spaces, Topology Proceedings, 25 (2000), 17–30.

    MATH  MathSciNet  Google Scholar 

  9. M. Caldas and G. Navalagi, Some remarks on weakly-semi-closed functions, J. Inst. Math. Comput. Sci. Math. Ser., 14 (2001), 107–110.

    MathSciNet  Google Scholar 

  10. M. Caldas and G. Navalagi, On weak forms of β-open and β-closed functions, Anal. St. Univ. Al. I. Cuza-Iaşi, s. Ia. Mat., 49 (2003), 115–128.

    MATH  MathSciNet  Google Scholar 

  11. M. Caldas and G. Navalagi, On weak forms of preopen and preclosed functions, Archivum Math., 40 (2004), 119–128.

    MATH  MathSciNet  Google Scholar 

  12. M. Caldas and G. Navalagi, Weakly α-open functions between topological spaces, Internat. J. Math. Math. Sci., 3 (2004), 39–51.

    MATH  MathSciNet  Google Scholar 

  13. F. Cammaroto and T. Noiri, On Λm-sets and related topological spaces, Acta Math. Hungar., 109 (2005), 261–279.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  15. S. G. Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math., 74 (1972), 233–254.

    MATH  MathSciNet  Google Scholar 

  16. A. S. Davis, Indexed systems of neighborhood for general topological spaces, Amer. Math. Monthly, 68 (1961), 886–893.

    Article  MATH  MathSciNet  Google Scholar 

  17. G. Di Maio and T. Noiri, Weak and strong forms of irresolute functions, Third National Conference on Topology (Italian) (Trieste, 1986), Rend. Circ. Mat. Palermo (2) Suppl. No. 18 (1988), 255–273.

    Google Scholar 

  18. C. Dorsett, Semi-regular spaces, Soochow J. Math., 8 (1982), 45–53.

    MATH  MathSciNet  Google Scholar 

  19. A. A. El-Atik, A study of some types of mappings on topological spaces, M.S. Thesis, Tanta Univ., Egypt, 1997.

    Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  22. Ch. Konstadilaki-Savvopoulou and D. Janković, R-continuous functions, Internat. J. Math. Math. Sci., 15 (1992), 57–64.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  24. P. E. Long and L. L. Herrington, Strongly θ-continuous functions, J. Korean Math. Soc., 18 (1981), 21–28.

    MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  28. M. Mocanu, Generalizations of open functions, Stud. Cerc. St. Ser. Mat., Univ. Bacǎau, 13 (2003), 67–78.

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  30. T. Noiri, On δ-continuous functions, J. Korean Math. Soc., 16 (1980), 161–166.

    MATH  MathSciNet  Google Scholar 

  31. T. Noiri, Weak and strong forms of β-irresolute functions, Acta Math. Hungar., 99 (2003), 315–328.

    Article  MATH  MathSciNet  Google Scholar 

  32. T. Noiri and V. Popa, On m-D-separation axioms, J. Fac. Sci. Univ. Istanbul, 61/62 (2002/2003), 15–28.

    MathSciNet  Google Scholar 

  33. T. Noiri and V. Popa, A unified theory of θ-continuity for functions, Rend. Circ. Mat. Palermo (2), 52 (2003), 163–188.

    MATH  MathSciNet  Google Scholar 

  34. T. Noiri and V. Popa, A unified theory for strong θ-continuity for functions, Acta Math. Hungar., 106 (2005), 167–186.

    Article  MATH  MathSciNet  Google Scholar 

  35. T. Noiri and V. Popa, A unified theory of weakly closed functions, Anal. St. Univ. “Al. I. Cuza” Iaşi, s. Ia. Mat., 51 (2005), 361–375.

    MATH  MathSciNet  Google Scholar 

  36. M. C. Pal and P. Bhattacharyya, Feeble and strong forms of preirresolute functions, Bull. Malaysian Math. Sci. Soc. (2), 19 (1996), 63–75.

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  38. V. Popa and T. Noiri, On M-continuous functions, Anal. Univ. “Dunarea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor., Fasc. II, 18(23) (2000), 31–41.

    Google Scholar 

  39. V. Popa and T. Noiri, On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ., 22 (2001), 9–18.

    MATH  MathSciNet  Google Scholar 

  40. V. Popa and T. Noiri, A unified theory of weak continuity for functions, Rend. Circ. Mat. Palermo (2), 51 (2002), 439–464.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  42. I. L. Reilly and M. K. Vamanamurthy, On α-continuity in topological spaces, Acta Math. Hungar., 45 (1985), 27–32.

    Article  MATH  MathSciNet  Google Scholar 

  43. D. A. Rose and D. S. Janković, Weakly closed functions and Hausdorff spaces, Math. Nachr., 130 (1987), 105–110.

    Article  MATH  MathSciNet  Google Scholar 

  44. N. V. Veličko, 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, Kumamoto-ken, 869-5142, Japan

    T. Noiri

  2. Department of Mathematics, University of Bacǎu, 600114, Bacǎu, Rumania

    V. Popa

Authors
  1. T. Noiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Popa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Noiri.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noiri, T., Popa, V. A unified theory of R-continuity. Acta Math Hung 118, 61–74 (2008). https://doi.org/10.1007/s10474-007-6155-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-007-6155-x

Key words and phrases

2000 Mathematics Subject Classification

Search

Navigation