Arcwise accessibility in hyperspaces

Sam B. Nadler, Jr.

Displaying similar documents to “Arcwise accessibility in hyperspaces”

Singular arc-like continua

Tadeusz Maćkowiak

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CONTENTSIntroduction.......................................................................................................51. Preliminaries.................................................................................................6 A. Mappings....................................................................................................6 B. Arc-like continua.........................................................................................8 C. Pseudosuspensions...................................................................................8 D....

On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

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For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum $S_{n, α, β}$ such that (a) $d i m S_{n, α, β} = n$ ; (b) $t r D g S_{n, α, β} = t r D g o S_{n, α, β} = α$ ; (c) $t r i n d S_{n, α, β} = t r I n d ₀ S_{n, α, β} = β$ ; (d) if β < ω(⁺), then $S_{n, α, β}$ is separable and first countable; (e) if n = 1, then $S_{n, α, β}$ can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then $S_{n, α, β}$ can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then $S_{n, α, β}$ can be made chainable and hereditarily indecomposable. In...

A continuum $X$ such that $C (X)$ is not continuously homogeneous

Alejandro Illanes (2016)

Commentationes Mathematicae Universitatis Carolinae

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A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p, q \in X$ there exists a continuous surjective function $f : X \to X$ such that $f (p) = q$ . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$ , $C (X)$ , is not continuously homogeneous.

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 (2018)

Commentationes Mathematicae Universitatis Carolinae

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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 $Z - {z}$ 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.

On the hyperspace $C_{n} (X) / {C_{n}}_{K} (X)$

José G. Anaya, Enrique Castañeda-Alvarado, José A. Martínez-Cortez (2021)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a continuum and $n$ a positive integer. Let $C_{n} (X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components, endowed with the Hausdorff metric. For $K$ compact subset of $X$ , define the hyperspace ${C_{n}}_{K} (X) = {A \in C_{n} (X) : K \subset A}$ . In this paper, we consider the hyperspace $C_{K}^{n} (X) = C_{n} (X) / {C_{n}}_{K} (X)$ , which can be a tool to study the space $C_{n} (X)$ . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility. ...

On connectivity properties of hyperspaces of $R_{0}$ spaces

M. Mršević (1979)

Matematički Vesnik

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Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^{X}$ can be extended to a Whitney map for $2^{X}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

On D-connected sets in the space $V^{q}$

S. Topa (1976)

Annales Polonici Mathematici

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On affinity of Peano type functions

Tomasz Słonka (2012)

Colloquium Mathematicae

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We show that if n is a positive integer and $2^{ℵ ₀} \leq ℵ ₙ$ , then for every positive integer m and for every real constant c > 0 there are functions $f ₁, . . ., f_{n + m} : ℝ ⁿ \to ℝ$ such that $(f ₁, . . ., f_{n + m}) (ℝ ⁿ) = ℝ^{n + m}$ and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that $(f_{i ₁}, . . ., f_{i ₙ}) (y) = y + w$ for $y \in x + (- c, c) \times ℝ^{n - 1}$ .

Global continuum of positive solutions for discrete $p$ -Laplacian eigenvalue problems

Dingyong Bai, Yuming Chen (2015)

Applications of Mathematics

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We discuss the discrete $p$ -Laplacian eigenvalue problem, $\{\begin{matrix} Δ (φ_{p} (Δ u (k - 1))) + λ a (k) g (u (k)) = 0, k \in {1, 2, ..., T}, \\ u (0) = u (T + 1) = 0, \end{matrix}$ where $T > 1$ is a given positive integer and $φ_{p} (x) : = {| x |}^{p - 2} x$ , $p > 1$ . First, the existence of an unbounded continuum $𝒞$ of positive solutions emanating from $(λ, u) = (0, 0)$ is shown under suitable conditions on the nonlinearity. Then, under an additional condition, it is shown that the positive solution is unique for any $λ > 0$ and all solutions are ordered. Thus the continuum $𝒞$ is a monotone continuous curve globally defined for all $λ > 0$ .

On starshapedness of the union of closed sets in $R^{n}$

Krzysztof Kołodziejczyk (1987)

Colloquium Mathematicae

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