Glasnik Matematicki, Vol. 49, No. 2 (2014), 421-432.

UNIQUENESS OF HYPERSPACES OF INDECOMPOSABLE ARC CONTINUA

Rodrigo Hernández-Gutiérrez, Alejandro Illanes and Verónica Martínez-de-la-Vega

Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, A.P. 61-3, Xangari, Morelia, Michoacán, 58089, México
e-mail: rod@matmor.unam.mx

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, 04510, D.F.
e-mail: illanes@matem.unam.mx

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, 04510, D.F.
e-mail: vmvm@matem.unam.mx


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)).

2010 Mathematics Subject Classification.   54B20, 54F15.

Key words and phrases.   Continuum, hyperspace, indecomposability, rigidity, unique hyperspace, wire.


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DOI: 10.3336/gm.49.2.14


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