Original scientific paper

https://doi.org/10.3336/gm.44.1.12

Dendrites and symmetric products

Gerardo Acosta ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., México
Rodrigo Hernández-Gutiérrez ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., México
Verónica Martinez-de-la-Vega ; Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., México

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 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.

Keywords

Continuum; contractibility; dendrite; finite graph; unique hyperspace

Hrčak ID:

36953

URI

https://hrcak.srce.hr/36953

Publication date:

21.5.2009.

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