호남수학학술지 (Honam Mathematical Journal)

  • 제46권4호
  • /
  • Pages.606-616
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  • 2024
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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STATISTICALLY ω-FRÉCHET AND STATISTICALLY ω-SEQUENTIAL SPACES: STATISTICAL CONVERGENCES OF ω-NETS

  • Junhui Kim (Department of Mathematics Education, Wonkwang University)
  • 투고 : 2024.02.23
  • 심사 : 2024.07.26
  • 발행 : 2024.12.20
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초록

In this paper, we introduce some modifications of statistically Fréchet and statistically sequential spaces which were defined in [5], termed statistically ω-Fréchet and statistically ω-sequential spaces concerned with ω-nets. Our work includes the construction of an illustrative example that distinguishes these two properties. Furthermore, we establish general relationships between statistically ω-Fréchet and statistically ω-sequential properties, demonstrating their equivalence in the class of statistically ω-transitive spaces.

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과제정보

I would like to express my sincere gratitude to the reviewers for their insightful comments and valuable suggestions, which greatly contributed to the improvement of this paper.

참고문헌

  1. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  2. J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
  3. R. E. Hodel, A theory of convergence and cluster points based on κ-nets, Topology Proc. 35 (2010), 291-330.
  4. P. Kostyrko, M. Macaj, T. Salat, and O. Strauch, On statistical limit points, Proc. Amer. Math. Soc. 129 (2000), 2647-2654.
  5. G. D. Maio and L. D. R. Kocinac, Statistical convergence in topology, Topology and its Appl. 156 (2008), 28-45.