Zhou, Xiangeng2026-05-252026-05-252026-03-161576-9402https://riunet.upv.es/handle/10251/233563[EN] 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 C?(X).The following main theorem is obtained. Theorem. Let ? 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-Fréchet-Urysohn space.Reconocimiento - No comercial - Compartir igual (by-nc-sa)I-Fréchet-Urysohn spacesstrongly I-Fréchet-Urysohn spacesstrictly IFréchet-Urysohn spacesCountable tightnessSet-open topologyFunctional spacesArtículo10.4995/agt.24158Abierto1989-4147