Original scientific paper

https://doi.org/10.3336/gm.49.2.14

Uniqueness of hyperspaces of indecomposable arc continua

Rodrigo Hernández-Gutiérrez ; Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, A.P. 61-3, Xangari, Morelia, Michoacán, 58089, México
Alejandro Illanes ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, 04510, D.F.
Verónica Martínez-de-la-Vega ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, 04510, D.F.

Abstract

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)).

Keywords

Continuum; hyperspace; indecomposability; rigidity; unique hyperspace; wire

Hrčak ID:

130894

URI

https://hrcak.srce.hr/130894

Publication date:

18.12.2014.

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