Induced near-homeomorphisms

Włodzimierz J. Charatonik

Displaying similar documents to “Induced near-homeomorphisms”

Mapping hierarchy for dendrites

J. J. Charatonik, W. J. Charatonik, J. R. Prajs

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AbstractLet a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define $Y \leq_{F} X$ if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order $\leq_{F}$ in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order $\leq_{F}$ , and characterize spaces...

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...

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.

Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets

Hisao Kato (1993)

Fundamenta Mathematicae

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We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions $W^{S} (x) | x \in X$ and $W^{(} u) (x) | x \in X$ of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, $W^{σ} (x)$ ...

Homeomorphisms of composants of Knaster continua

Sonja Štimac (2002)

Fundamenta Mathematicae

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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.

Krasinkiewicz maps from compacta to polyhedra

Eiichi Matsuhashi (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that the set of all Krasinkiewicz maps from a compact metric space to a polyhedron (or a 1-dimensional locally connected continuum, or an n-dimensional Menger manifold, n ≥ 1) is a dense $G_{δ}$ -subset of the space of all maps. We also investigate the existence of surjective Krasinkiewicz maps from continua to polyhedra.