Glasnik Matematicki, Vol. 44, No.1 (2009), 195-210.

DENDRITES AND SYMMETRIC PRODUCTS

Gerardo Acosta, Rodrigo Hernández-Gutiérrez and Verónica Martinez-de-la-Vega

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., 04510, México
e-mail: gacosta@matem.unam.mx
e-mail: rod@matem.unam.mx
e-mail: vmvm@matem.unam.mx

Abstract.   For a given continuum X and a natural number n, we consider the hyperspace Fn(X) of all nonempty subsets of X with at most n points, metrized by the Hausdorff metric. In this paper we show that if X is a dendrite whose set of end points is closed, n in N and Y is a continuum such that the hyperspaces Fn(X) and Fn(Y) are homeomorphic, then Y is a dendrite whose set of end points is closed.

2000 Mathematics Subject Classification.   54B20, 54C15, 54F15, 54F50.

Key words and phrases.   Continuum, contractibility, dendrite, finite graph, unique hyperspace.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.1.12

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