| Contractibility of Hyperspaces Ck（X） |
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| 作者姓名： | CAO Jin-wen LI Yan JIA Yong-jin |
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| 作者单位： | [1]College of Information Management, Sichuan Province Key Laboratory of Mathematicsgeology, Chengdu University of Technology, Chengdu 610059, China. [2]College of Animal Science, Anhui Science and Technology University, Fengyang 233100, China |
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| 基金项目： | Supported by the Department of Education Sichuan Province Foundation for Science Research（2006C041）; Supported by the Anhui Provincial Foundation for Young Talents in College（2010SQRL158） |
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| 摘 要： | This paper proves the following results： let X be a continuum, let k, m ∈ N, and let B ∈ C m （X）, consider the continuous surjection f k ： C k （X） → C k （X）. We define the mapping B ： C k （X） → C k＋m （X）： by B （A） = f k （A） B. Then following assertions are equivalent： （1） The hyperspace C k （X） is g-contractible; （2） For each m ∈ N and for each B ∈ C m （X） the mapping B is a W -deformation in C k＋m （X）; （3） For each m ∈ N there exists B ∈ C m （X） such that the mapping B is a W -deformation in C k＋m （X）; （4） There exists m ∈ N such that for each B ∈ C m （X） the mapping B is a W -deformation in C k＋m （X）; （5） There exist m ∈ N and B ∈ C m （X） such that the mapping B is a W -deformation in C k＋m （X）.
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| 关 键 词： | continuum hyperspaces g-contractible W -deformation mapping |
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