The Suslinian number and other cardinal invariants of continua

T. Banakh; V. V. Fedorchuk; J. Nikiel; M. Tuncali

Displaying similar documents to “The Suslinian number and other cardinal invariants of continua”

Monotone retractions and depth of continua

Janusz Jerzy Charatonik, Panayotis Spyrou (1994)

Archivum Mathematicum

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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 continua with exactly n autohomeomorphisms

Elżbieta Pol (2002)

Colloquium Mathematicae

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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.

Weight and metrizability of inverses under hereditarily irreducible mappings.

Lončar, Ivan (2008)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Continua with unique symmetric product

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

Commentationes Mathematicae Universitatis Carolinae

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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...

On indecomposability and composants of chaotic continua

Hisao Kato (1996)

Fundamenta Mathematicae

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A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that $d (f^{n} (x), f^{n} (y)) > c$ . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that $d i a m i f^{n} (A) > c$ . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua...