Finite graphs have unique symmetric products

  • Castañeda E
  • Illanes A
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Abstract

Let X be a metric continuum and let Fn(X) be the nth symmetric product of X(Fn(X) is the hyperspace of nonempty subsets of X with at most n points). In this paper we prove that if Fn(X) is homeomorphic to Fn(Y), where X is a finite graph and Y is a continuum, then X is homeomorphic to Y. © 2005 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Continuum
  • Finite graphs
  • Hyperspaces
  • Symmetric products
  • Unique hyperspaces

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