Making holes in the cone, suspension and hyperspaces of some continua

José G. Anaya; Enrique Castañeda-Alvarado; Alejandro Fuentes-Montes de Oca; Fernando Orozco-Zitli

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 343-364
  • ISSN: 0010-2628

Abstract

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A connected topological space Z is unicoherent provided that if Z = A ∪ B where A and B are closed connected subsets of Z , then A ∩ B is connected. Let Z be a unicoherent space, we say that z ∈ Z makes a hole in Z if Z - { z } is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.

How to cite

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Anaya, José G., et al. "Making holes in the cone, suspension and hyperspaces of some continua." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 343-364. <http://eudml.org/doc/294553>.

@article{Anaya2018,
abstract = {A connected topological space $Z$ is unicoherent provided that if $Z=A\cup B$ where $A$ and $B$ are closed connected subsets of $Z$, then $A\cap B$ is connected. Let $Z$ be a unicoherent space, we say that $z\in Z$ makes a hole in $Z$ if $Z-\lbrace z\rbrace $ is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.},
author = {Anaya, José G., Castañeda-Alvarado, Enrique, Oca, Alejandro Fuentes-Montes de, Orozco-Zitli, Fernando},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {continuum; hyperspace; hyperspace suspension; property (b); unicoherence; cone; suspension},
language = {eng},
number = {3},
pages = {343-364},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Making holes in the cone, suspension and hyperspaces of some continua},
url = {http://eudml.org/doc/294553},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Anaya, José G.
AU - Castañeda-Alvarado, Enrique
AU - Oca, Alejandro Fuentes-Montes de
AU - Orozco-Zitli, Fernando
TI - Making holes in the cone, suspension and hyperspaces of some continua
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 343
EP - 364
AB - A connected topological space $Z$ is unicoherent provided that if $Z=A\cup B$ where $A$ and $B$ are closed connected subsets of $Z$, then $A\cap B$ is connected. Let $Z$ be a unicoherent space, we say that $z\in Z$ makes a hole in $Z$ if $Z-\lbrace z\rbrace $ is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.
LA - eng
KW - continuum; hyperspace; hyperspace suspension; property (b); unicoherence; cone; suspension
UR - http://eudml.org/doc/294553
ER -

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