DOI QR코드

DOI QR Code

A UNIFIED FORM OF SEVERAL GENERALIZATIONS OF TRANSITIVE FUNCTIONS

  • Received : 2025.01.10
  • Accepted : 2025.05.23
  • Published : 2025.10.31

Abstract

We introduce the concept of m-transitivity and study some of the properties and the relation with some other types of generalizations of transitivity. We prove that the m-transitivity is a unified form of the classical transitivity and many other types of transitivity such as 𝛿-transitive, 𝛼-transitive, b-transitive, and e*-transitive.

Keywords

References

  1. M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, β-open sets and β-continuous mapping, Bull. Fac. Sci. Assiut Univ. A 12 (1983), no. 1, 77–90.
  2. D. Andrijevi´c, On b-open sets, Mat. Vesnik 48 (1996), no. 1-2, 59–64.
  3. M. Baloush, T. Noiri, and S. C. Dzui-Kifli, Exploring e∗-transitivity: bridging classical and novel chaos notions, JQMA 21(2)(2025), 15–26.
  4. E. Ekici, On e∗-open sets and (D, S)∗-sets, Math. Morav. 13 (2009), no. 1, 29–36. https://doi.org/10.5937/matmor0901029e
  5. E. Hatır and T. Noiri, Decompositions of continuity and complete continuity, Acta Math. Hungar. 113 (2006), no. 4, 281–287. https://doi.org/10.1007/s10474-006-0105-x
  6. E. Hatır and T. Noiri, On δ−β-continuous functions, Chaos Solitons Fractals 42 (2009), no. 1, 205–211. https://doi.org/10.1016/j.chaos.2008.11.008
  7. J. E. Joseph, Characterizations of nearly-compact spaces, Boll. Unione Mat. Itali, B (5) 13 (1976), no. 2, 311–321.
  8. M. Kaki, New types of δ-transitive maps, Int. J. Eng. Tech. 12(6) (2012), 134–136.
  9. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41. https://doi.org/10.2307/2312781
  10. S. N. Maheshwari and S. S. Thakur, On α-irresolute mappings, Tamkang J. Math. 11 (1980), no. 2, 209–214.
  11. H. Maki, K. Chandrasekhara Rao, and A. Nagoor Gani, On generalizing semi-open sets and preopen sets, Pure Appl. Math. Sci. 49 (1999), no. 1-2, 17–29.
  12. A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt No. 53 (1982), 47–53 (1983).
  13. M. Murad, Topologically α-transitive maps and minimal systems, Gen. Math. Notes 10(2) (2012) 43–53.
  14. M. Murad, New types of transitive functions and minimal systems, Int. J. Basic Appl. Sci. 12(4) (2012) 53–58.
  15. O. Nj˚astad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961–970. http://projecteuclid.org/euclid.pjm/1102995581 102995581
  16. T. Noiri, On δ-continuous functions, J. Korean Math. Soc. 16 (1979/80), no. 2, 161–166.
  17. V. Popa and T. Noiri, On M-continuous functions, Anal. Univ. "Dunărea de Jos" Galąti, Ser. Mat. Fiz. Mec. Teor., Fasc. II 18 (23) (2000), 31–41.
  18. V. Popa and T. Noiri, On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 22 (2001), 9–18.
  19. V. Popa and T. Noiri, A unified theory of weak continuity for functions, Rend. Circ. Mat. Palermo (2) 51 (2002), no. 3, 439–464. https://doi.org/10.1007/BF02871853
  20. N. V. Veliˇcko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968), 103–118.