Uniqueness of hyperspaces of indecomposable arc continua

Uniqueness of hyperspaces of indecomposable arc continua

Given a metric continuum X, we consider the hyperspace Cn(X) of all nonempty closed subsets of X with at most n components. In this paper we prove that if n≠ 2, X is an indecomposable continuum such that all its proper nondegenerate subcontinua are arcs and Y is a continuum such that Cn(X) is homeom...

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Veröffentlicht in:Glasnik matematički 2014-12, Vol.49 (2), p.421-432
Hauptverfasser: Hernández-Gutiérrez, Rodrigo, Illanes, Alejandro, Martínez-de-la-Vega, Verónica
Format: Artikel
Sprache:eng
Schlagworte:
Continuum
hyperspace
indecomposability
rigidity
unique hyperspace
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Zusammenfassung:Given a metric continuum X, we consider the hyperspace Cn(X) of all nonempty closed subsets of X with at most n components. In this paper we prove that if n≠ 2, X is an indecomposable continuum such that all its proper nondegenerate subcontinua are arcs and Y is a continuum such that Cn(X) is homeomorphic to Cn(Y), then X is homeomorphic to Y (that is, X has unique hyperspace Cn(X)).
ISSN:0017-095X
1846-7989
DOI:10.3336/gm.49.2.14