Results 1 to 10 of about 97 (87)
Topology and Its Applications, 1986 Following the terminology of the author we call a singularity of metric continua singularity R if the continuum contains a certain kind of continua as introduced and studied by \textit{S. T. Czuba} [Bull. Acad. Pol. Sci., Sér. Sci. Math. 27, 299-302 (1979; Zbl 0424.54026)].
Włodzimierz J Charatonik
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On the hyperspaces of meager and regular continua
Applied General TopologyGiven a metric continuum X, we consider the collection of all regular subcontinua of X and the collection of all meager subcontinua of X, these hyperspaces are denoted by D(X) and M(X), respectively.
Javier Camargo +2 more
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On hyperspaces of non-cut sets of continua
Topology and Its Applications, 2017 For a metric continuum \(X\), \(2^X\) denotes the hyperspace of nonempty closed subsets of \(X\), and \(F_{1}(X)\) is the hyperspace of singletons of \(X\), both hyperspaces are endowed with the Hausdorff metric. Given an element \(A \neq X\) in \(2^X\), we say that \(A\): (a) is a non-weak cut set of \(X\) (\(A \in NWC(X)\)) provided that for any two ...
Raúl Escobedo +1 more
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Making holes in the cone, suspension and hyperspaces of some continua [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2018 A connected space is unicoherent if \(A\cap B\) is connected for every pair of closed connected subsets \(A\) and \(B\) whose union is \(Z\). A point \(z\) in a unicoherent space \(Z\) makes a hole in \(Z\) if \(Z\setminus\{z\}\) is connected and non-unicoherent.
Anaya, José G. +3 more
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Continua with cones homeomorphic to hyperspaces
Topology and Its Applications, 1973 AbstractWe investigate continua with the property that the cone over the continuum is homeomorphic to the hyperspace of subcontinua of the continuum. Among our results are the following theorems: (i)Such a finite-dimensional continuum must be atriodic and one-dimensional; (ii)if such a continuum is hereditarily decomposable, then it must be an arc, an ...
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Hyperspaces of Peano continua are Hubert cubes [PDF]
Fundamenta Mathematicae, 1978 Curtis, D. W., Schori, R. M.
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On the hyperspaces of hereditarily indecomposable continua [PDF]
Fundamenta Mathematicae, 1974 J Krasinkiewicz
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Continua whose hyperspace of subcontinua is infinite dimensional and a cone
Extracta Mathematicae, 2023 We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.
S. Macías, S.B. Nadler
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Applied General Topology, 2023 In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of
Qays R. Shakir
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Hyperspaces of continua with connected boundaries in π-Euclidean Peano continua [PDF]
Topology and its Applications, 2020 Let $X$ be a nondegenerate Peano unicoherent continuum. The family $CB(X)$ of proper subcontinua of $X$ with connected boundaries is a $G_δ$-subset of the hyperspace $C(X)$ of all subcontinua of $X$. If every nonempty open subset of $X$ contains an open subset homeomorphic to $\mathbb R^n$ (such space is called $π$-$n$-Euclidean) and $2\le ...
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