On colocal connectedness of $F_1(X)$ in $F_2(X)$

Mauricio Chacón-Tirado; César Piceno

doi:10.4064/cm9420-9-2024

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / Online First articles

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On colocal connectedness of $F_1(X)$ in $F_2(X)$

Volume 176 / 2024

Mauricio Chacón-Tirado, César Piceno Colloquium Mathematicum 176 (2024), 171-175 MSC: Primary 54B20; Secondary 54F15 DOI: 10.4064/cm9420-9-2024 Published online: 14 November 2024

Abstract

We show that the arc is the unique chainable continuum $X$ such that $F_1(X)$ is a set of colocal connectedness of $F_2(X)$ . Also, we give a non-locally-connected continuum $X$ whose hyperspace $F_1(X)$ is a set of colocal connectedness of $F_2(X)$ , answering negatively a question posed by Martínez-de-la-Vega and J. M. Martínez-Montejano (2020).

Authors

Mauricio Chacón-TiradoFacultad de Ciencias Físico Matemáticas
Benemérita Universidad Autónoma de Puebla
C.P. 72570, Puebla, Mexico
e-mail
César PicenoFacultad de Ciencias Físico Matemáticas
Benemérita Universidad Autónoma de Puebla
C.P. 72570, Puebla, Mexico
e-mail

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Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / Online First articles

Colloquium Mathematicum

On colocal connectedness of F_1(X) in F_2(X)F_2(X)

Volume 176 / 2024

Abstract

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On colocal connectedness of $F_1(X)$ in $F_2(X)$