Results 101 to 110 of about 239 (123)
Hyperspaces of Peano continua of euclidean spaces
Fundamenta Mathematicae, 1993 Pour un espace métrique \(X\), soit \(C(X)\) l'espace des sous-continus non vides de \(X\) avec la topologie de Vietoris, et soit \(L(X)\) le sous-espace de \(C(X)\) formé des continus péaniens. Les auteurs montrent que, pour \(n \geq 3\), \(L(\mathbb{R}^ n)\) est homéomorphe au produit dénombrable \(B^ \infty\), où \(B\) est le pseudo-bord du cube de ...
Jan Van Mill
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Some Properties of Hyperspaces with Applications to Continua Theory
Canadian Journal of Mathematics, 1979 In 1972, Lelek introduced the notion of Class (W) in his seminar at the University of Houston [see below for definitions of concepts mentioned here]. Since then there has been much interest in classifying and characterizing continua in Class (W). For example, Cook has a result [5, Theorem 4] which implies that any hereditarily indecomposible continuum ...
Grispolakis, J. +2 more
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ON UNICOHERENCE AND CONTRACTIBILITY OF HYPERSPACES OF NONMETRIZABLE CONTINUA
Rocky Mountain Journal of Mathematics, 2023For a Hausdorff continuum (i.e., a nondegenerate compact connected Hausdorff space) \(X\), let \(C (X)\) denote the space of all subcontinua of \(X\) endowed with the Vietoris topology. A metrizable Hausdorff continuum is called a continuum. In this paper, the author discusses generalizations of theorems on unicoherence and contractibility of \(C(X ...
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Hyperspaces of generalized continua which are infinite cylinders
Topology and Its Applications, 2019 We deal with an analogue of the cone = hyperspace property for generalized continua. Namely, we study the class Cyl of those generalized continua X for which the hyperspace C(X) is homeomorphic to the infinite cylinder X x ℝ≥ 0.
Tomáš FernÁndez-Bayort
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Problems on hyperspaces of continua, some answers
Topology and its Applications, 2022For a metric continuum \(X\) let the symbol \(F_{n}(X)\) denote the \(n\)-fold symmetric product of \(X\), the symbol \(C_{n}(X)\) the \(n\)-fold hyperspace of \(X\), the symbol \(\mathcal{M}(X)\) the hyperspace of arcs and singletons of \(X\). A continuum \(X\) is said to be \(k\)-mutually aposyndetic provided that given \(k\) distinct points, there ...
Illanes, Alejandro +2 more
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Uniqueness of the (n,m)-fold hyperspace suspension for continua
Topology and its Applications, 2023Let \(n,m\in\mathbb{N}\) with \(m\leq n\) and let \(X\) be a continuum (a compact, connected and non-empty metric space). The symbols \(C_{n}(X)\) and \(F_{n}(X)\) denote the hyperspaces of all nonempty closed subsets of \(X\) with at most \(n\) components, and with at most \(n\) points of \(X\), respectively, both with the Hausdorff metric. The \((n,m)
Hernández-Valdez, Gerardo +3 more
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Kelley continua and the hyperspace Λ(X)
Topology and its Applications, 2019Abstract Using the Kelley function G, the hyperspace Λ ( X ) is defined. We prove that Λ ( X ) is homeomorphic to X whenever X is a Kelley continuum. The elements of Λ ( X ) are used to prove that G is a continuous surjection if X is an atriodic Kelley continuum.
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Involutions of Hilbert cubes that are hyperspaces of Peano continua
Topology and its Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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