I-Fréchet-Urysohn property in Cα(X)

[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.