Contractibility of the hyperspace of meager subcontinua, two examples

• Illanes, Alejandro ^[1] ; Ramírez Angarita, Diego Alexander ^[1]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 657-670
• Idioma: inglés
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• Resumen

  • 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.