C1(X) on the edge of C2(X)

Sergio Macías

https://orcid.org/0000-0001-7464-8852

Mexico

Universidad Nacional Autónoma de México image/svg+xml

David Maya

https://orcid.org/0000-0002-0319-9313

Mexico

Universidad Autónoma del Estado de México image/svg+xml

Submitted: 2024-06-29

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Accepted: 2024-12-12

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Published: 2025-04-01

DOI: https://doi.org/10.4995/agt.2025.22003

Copyright (c) 2025 Javier Camargo, Sergio Macías, David Maya

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

composant, continuum, continuum of colocal connectedness, continuumwise connected space, hyperspace, n-fold hyperspace, property of Kelley, property of Kelley weakly, not a strong centre, pseudo-arc, set function T, shore subcontinuum, union composant, T-closed set, T-closed subcontinuum, strongly continuumwise connected space

Supporting agencies:

Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

Universidad Industrial de Santander

Abstract:

Given a continuum X and a positive integer n, let Cn(X) be the hyperspace consisting of all nonempty closed subsets of X having at most n components. For a subcontinuum A of X having empty interior, consider the following properties: A is a subcontinuum of colocal connectedness, X\A is continuumwise connected, A is a nonblock subcontinuum, A is a shore subcontinuum, A is not a strong centre. In this paper, we prove that C1(X) has all of these properties in Cn(X) if n ≥ 3, and we study when C1(X) has one of these properties in C2(X) .

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