数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 526-529.
摘要: This paper proves the following results: let X be a continuum, let k, m ∈ N, and let B ∈ Cm(X), consider the continuous surjection fk: Ck(X) → Ck(X). We define the mapping B : Ck(X) → Ck+m(X): by B (A) = fk(A) B. Then following assertions are equivalent: (1) The hyperspace Ck(X) is g-contractible; (2) For each m ∈ N and for each B ∈ Cm(X) the mapping B is a W-deformation in Ck+m(X); (3) For each m ∈ N there exists B ∈Cm(X) such that the mapping B is a W-deformation in Ck+m(X); (4) There exists m ∈ N such that for each B ∈ Cm(X) the mapping B is a W-deformation in Ck+m(X); (5) There exist m ∈ N and B ∈ Cm(X) such that the mapping B is a W-deformation in Ck+m(X).
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