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On the uniqueness of the n-fold pseudo-hyperspace suspension for locally connected continua
Topology and Its Applications, 2022A continuum is a compact connected nondegenerate metric space. By a hyperspace of a continuum \(X\) we mean a specified collection of subsets of \(X\) endowed with the Hausdorff metric. Given a continuum and \(n\in \mathbb N\), we consider its hyperspaces: \[ \begin{aligned} 2^{X} &= \{A\subseteq X \mid A \text{ is closed and nonempty}\},\\ \mathcal{C ...
Fernando Macías-Romero +1 more
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Absolute n-fold hyperspace suspensions
Colloquium Mathematicum, 2006The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension.
Sérgio Macias, Sam B Nadler
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On the symmetric hyperspace of the circle [PDF]
Topology and Its Applications, 2010 By X(n), n⩾1, we denote the n-th symmetric hyperspace of a metric space X as the space of non-empty finite subsets of X with at most n elements endowed with the Hausdorff metric.
Akira Koyama
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Topological properties on n-fold pseudo-hyperspace suspension of a continuum
Topology and Its Applications, 2020Given a metric continuum \(X\) let \(C_{n}(X)\) denote the hyperspace of nonempty closed subsets of \(X\) having at most \(n\) components and \(F_{1}(X)\) the space of singletons of \(X\), both endowed with the Hausdorff metric. The quotient continuum \(C_{n}(X)/F_{1}(X)\) is denoted by \(\mathrm{PHS}_{n}(X)\) and is called the pseudo-hyperspace ...
Santiago-Santos, Alicia +1 more
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Colloquium Mathematicum, 2018
In this work, continua are taken to be metric; a \(k\)-od is defined to be a continuum \(B\) having a subcontinuum \(A\) where \(B\setminus A\) has at least \(k\) components. For each continuum \(X\), \(C_n(X)\) denotes the hyperspace of non-empty closed subsets of \(X\) with at most \(n\) components, the so-called \(n\)-fold hyperspace.
Illanes, Alejandro +1 more
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In this work, continua are taken to be metric; a \(k\)-od is defined to be a continuum \(B\) having a subcontinuum \(A\) where \(B\setminus A\) has at least \(k\) components. For each continuum \(X\), \(C_n(X)\) denotes the hyperspace of non-empty closed subsets of \(X\) with at most \(n\) components, the so-called \(n\)-fold hyperspace.
Illanes, Alejandro +1 more
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Induced Maps on n-Fold Hyperspaces
2018We begin considering some classes of maps between continua proving some of their general properties. Then we consider the following problem: Let \({\mathcal {A}}\) be class of maps. What are the relationships between the following statements: (1) \(f\in {\mathcal {A}}\); (2) \({\mathcal {C}}_n(f)\in {\mathcal {A}}\); (3) \
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Cells and $n$-fold hyperspaces
Colloquium Mathematicum, 2016Sergio Macías +2 more
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Uniqueness of the (n,m)-fold hyperspace suspension for continua
Topology and Its Applications, 2023David Herrera-Carrasco +1 more
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The metric mean dimension of hyperspace induced by symbolic dynamical systems
International Journal of General Systems, 2022Xiaojun Huang, Xian Wang
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12-Homogeneous n-fold hyperspace suspensions
Topology and Its Applications, 2015Sérgio Macias +1 more
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