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- W2045987921 abstract "Let C ( X ) and 2 X denote the hyperspaces of subcontinua and of closed subsets of a metric continuum X , respectively. For p ∈ X , define the hyperspace 2 X p ={A∈2 X : p∈A} . Moreover, consider the mapping A ↦ A ∪{ p }. In this paper we find necessary and sufficient conditions under which this mapping is a deformation retraction or a strong deformation retraction from 2 X onto 2 X p . We obtain similar results for the case in which the domain of the mapping is C ( X ). Finally, we characterize local connectedness of a continuum in terms of the behavior of these mappings." @default.
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- W2045987921 date "2004-01-01" @default.
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- W2045987921 title "Retractions in hyperspaces" @default.
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- W2045987921 doi "https://doi.org/10.1016/s0166-8641(03)00193-7" @default.
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