On the set function $\wp $

Sergio Macías

The search session has expired. Please query the service again.

Displaying similar documents to “On the set function $℘$ ”

Homeomorphisms of composants of Knaster continua

Sonja Štimac (2002)

Fundamenta Mathematicae

Similarity:

The Knaster continuum $K_{p}$ is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of $K_{p}$ having no endpoints are homeomorphic. This generalizes Bandt’s result which concerns the case p = 2.

Decompositions of the plane and the size of the continuum

Ramiro de la Vega (2009)

Fundamenta Mathematicae

Similarity:

We consider a triple ⟨E₀,E₁,E₂⟩ of equivalence relations on ℝ² and investigate the possibility of decomposing the plane into three sets ℝ² = S₀ ∪ S₁ ∪ S₂ in such a way that each $S_{i}$ intersects each $E_{i}$ -class in finitely many points. Many results in the literature, starting with a famous theorem of Sierpiński, show that for certain triples the existence of such a decomposition is equivalent to the continuum hypothesis. We give a characterization in ZFC of the triples for which the decomposition...

Continua with unique symmetric product

José G. Anaya, Enrique Castañeda-Alvarado, Alejandro Illanes (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $X$ be a metric continuum. Let $F_{n} (X)$ denote the hyperspace of nonempty subsets of $X$ with at most $n$ elements. We say that the continuum $X$ has unique hyperspace $F_{n} (X)$ provided that the following implication holds: if $Y$ is a continuum and $F_{n} (X)$ is homeomorphic to $F_{n} (Y)$ , then $X$ is homeomorphic to $Y$ . In this paper we prove the following results: (1) if $X$ is an indecomposable continuum such that each nondegenerate proper subcontinuum of $X$ is an arc, then $X$ has unique hyperspace $F_{2} (X)$ , and (2) let $X$ be an arcwise...

A note on the paper ``Smoothness and the property of Kelley''

Gerardo Acosta, Álgebra Aguilar-Martínez (2007)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let $X$ be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, , Comment. Math. Univ. Carolin. (2000), no. 1, 123–132, it is claimed that $L (X) = ⋂_{p \in X} S (p)$ , where $L (X)$ is the set of points at which $X$ is locally connected and, for $p \in X$ , $a \in S (p)$ if and only if $X$ is smooth at $p$ with respect to $a$ . In this paper we show that such equality is incorrect and that the correct equality is $P (X) = ⋂_{p \in X} S (p)$ , where $P (X)$ is the set of points at which $X$ is connected im kleinen. We also use the correct equality to obtain some...

Hereditarily indecomposable continua with exactly n autohomeomorphisms

Elżbieta Pol (2002)

Colloquium Mathematicae

Similarity:

The main goal of this paper is to construct, for every n,m ∈ ℕ, a hereditarily indecomposable continuum $X_{n m}$ of dimension m which has exactly n autohomeomorphisms.

Monotone retractions and depth of continua

Janusz Jerzy Charatonik, Panayotis Spyrou (1994)

Archivum Mathematicum

Similarity:

It is shown that for every two countable ordinals $α$ and $β$ with $α > β$ there exist $λ$ -dendroids $X$ and $Y$ whose depths are $α$ and $β$ respectively, and a monotone retraction from $X$ onto $Y$ . Moreover, the continua $X$ and $Y$ can be either both arclike or both fans.

Hereditarily indecomposable inverse limits of graphs

K. Kawamura, H. M. Tuncali, E. D. Tymchatyn (2005)

Fundamenta Mathematicae

Similarity:

We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map $f_{ε} : G \to G$ which is ε-close to f such that the inverse limit $(G, f_{ε})$ is hereditarily indecomposable.

On topological factors of 3 dimensional locally connected continuum embeddable in $E^{3}$

Witold Rosicki (1978)

Fundamenta Mathematicae

Similarity:

Arcwise accessibility in hyperspaces

Sam B. Nadler, Jr.

Similarity:

CONTENTS1. Introduction........................................................................................................ 52. Segmentwise accessibility..................................................................................... 73. Arcwise accessibility of singletons....................................................................... 84. Compacta in X which arcwise disconnect $2^{X}$ or C(X)................................ 155. Hereditary indecomposability and arcwise accessibility.....................................

Displaying similar documents to “On the set function ℘ ”

Displaying similar documents to “On the set function $℘$ ”