Contractibility of the hyperspace of meager subcontinua, two examples
Submitted: 2024-08-10
|Accepted: 2025-03-10
|Published: 2025-10-01
Copyright (c) 2025 Alejandro Illanes, Diego Alexander Ramírez Angarita
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
Arc-smooth continuum, Continuum, Contractible, Dendroid, Hyperspace, Meager subcontinuum
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Abstract:
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.
References:
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