Rigidity of symmetric products |
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Authors: | Rodrigo Herná ndez-Gutié rrez,Veró nica Martí nez-de-la-Vega |
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Affiliation: | 1. Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, A.P. 61-3, Xangari, Morelia, Michoacán, 58089, Mexico;2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, D.F., 04510, Mexico |
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Abstract: | Given a metric continuum X, we consider the following hyperspaces of X : 2X, Cn(X) and Fn(X) (n∈N). Let F1(X)={{x}:x∈X}. A hyperspace K(X) of X is said to be rigid provided that for every homeomorphism h:K(X)→K(X) we have that h(F1(X))=F1(X). In this paper we study under which conditions a continuum X has a rigid hyperspace Fn(X). |
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Keywords: | primary, 54B20 secondary, 54F15 |
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