Monotone retractions and depth of continua

Janusz Jerzy Charatonik; Panayotis Spyrou

Displaying similar documents to “Monotone retractions and depth of continua”

The Suslinian number and other cardinal invariants of continua

T. Banakh, V. V. Fedorchuk, J. Nikiel, M. Tuncali (2010)

Fundamenta Mathematicae

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By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family ℂ of non-degenerate subcontinua of size |ℂ| > κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)⁺ and is the limit of an inverse well-ordered spectrum of length ≤ Sln(X)⁺, consisting of compacta with weight...

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.

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...

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

Gerardo Acosta, Álgebra Aguilar-Martínez (2007)

Commentationes Mathematicae Universitatis Carolinae

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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...

Absolutely terminal continua and confluent mappings

Janusz Jerzy Charatonik (1991)

Commentationes Mathematicae Universitatis Carolinae

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Interrelations between three concepts of terminal continua and their behaviour, when the underlying continuum is confluently mapped, are studied.

The hereditary classes of mappings

T. Maćkowiak (1977)

Fundamenta Mathematicae

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Continua determined by mappings.

Charatonik, Janusz J., Charatonik, Wlodzimierz J. (2000)

Publications de l'Institut Mathématique. Nouvelle Série

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