On the symmetric hyperspace of the circle

Naotsugu Chinen*, Akira Koyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


By X(n), n≤1, we denote the n-th symmetric hyperspace of a metric space X as the space of non-empty finite subsets of X with at most n elements endowed with the Hausdorff metric. In this paper we shall describe the n-th symmetric hyperspace S1(n) as a compactification of an open cone over σDn-2, here Dn-2 is the higher-dimensional dunce hat introduced by Andersen, Marjanović and Schori (1993) [2] if n is even, and Dn-2 has the homotopy type of Sn-2 if n is odd (see Andersen et al. (1993) [2]). Then we can determine the homotopy type of S1(n) and detect several topological properties of S1(n).

Original languageEnglish
Pages (from-to)2613-2621
Number of pages9
JournalTopology and its Applications
Issue number17
Publication statusPublished - 2010 Nov
Externally publishedYes


  • Compactification
  • Dunce hat
  • Symmetric hyperspace
  • Symmetric product

ASJC Scopus subject areas

  • Geometry and Topology


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