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Constructed dendroids demonstrate the lack of a link between contractibility of metric continuum and hyperspace of subcontinua.
Given a metric continuum X, the hyperspace of meager subcontinua of X, denoted by M(X), is the collection of all subcontinua of X with empty interior. Answering questions by Norberto Ordo˜nez, in this paper we construct two dendroids showing that there is no implication between the conditions: (a) X is contractible and (b) M(X) is contractible. We also prove that if X is an arc-smooth continuum, then M(X) is contractible.
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Illanes et al. (2025) studied this question.
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