The hyperspace of closed subsets on the edge of irreducible continua

• Capulín, Félix ^[1] ; Maya, David ^[1] ; Orozco-Zitli, Fernando ^[1] ; Rodríguez-Anaya, Emiliano ^[1]
  1. [1] Universidad Autónoma del Estado de México

     Universidad Autónoma del Estado de México

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 895-905
• Idioma: inglés
• DOI: 10.4995/agt.2025.24058
• Enlaces
  • Texto completo
• Resumen

  • For a nonempty nowhere dense closed subset of a continuum $X$, consider the following properties: being a non-weak cut subset, a non-block subset, a weak non-block subset, a shore subset, a non-strong center, and a non-cut subset of X. In this paper, we provide necessary conditions for subsets of an irreducible continuum about a subset to have one of these properties, and we prove that these properties are equivalent for nonempty nowhere dense closed subsets of an irreducible continuum about a finite subset. This result completes the study previously conducted on non-cut points and for subsets on the edge of a continuum by several authors.

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