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Retractions and contractibility in hyperspaces |
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| Authors: | Janusz J Charatonik Patricia Pellicer-Covarrubias |
| Institution: | a Instituto de Matemáticas, UNAM, Ciudad Universitaria, México, DF 04510, Mexico b Mathematical Institute, University of Wroc?aw, pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland c Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, DF 04510, Mexico |
| Abstract: | Given a metric continuum X, let X2 denote the hyperspace of all nonempty closed subsets of X. For each positive integer k let Ck(X) stand for the hyperspace of members of X2 having at most k components. Consider mappings  (where B∈Cm(X)) and  both defined by A?A∪B. We give necessary and sufficient conditions under which these mappings are deformation retractions (under a special convention for φB). The conditions are related to the contractibility of the corresponding hyperspaces. |
| Keywords: | 54B20 54C15 54F15 |
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