I-Fréchet-Urysohn property in Cα(X)

• Zhou, Xiangeng ^[1]
  1. [1] Ningde Normal University

     Ningde Normal University

     China

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.4995/agt.24158
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in Cα(X).The following main theorem is obtained.

    Theorem. Let α be a network of X. The following are equivalent.

    (1) Cα(X) is a strictly I-Fr´echet-Urysohn space.

    (2) Cα(X) is a strongly I-Fr´echet-Urysohn space.

    (3) Cα(X) is an I-Fr´echet-Urysohn space.

    (4) Every open α-cover of X contains an I-α-sequence.

    (5)  If {Un}n∈N  is a sequence of open α-cover of X, then there is an I-α-sequence {un}n∈N of X such that each un ∈ Un.

    (6) Cωα (X) is a strictly I-Fr´echet-Urysohn space.

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