Abstract
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 language | English |
---|---|
Pages (from-to) | 2613-2621 |
Number of pages | 9 |
Journal | Topology and its Applications |
Volume | 157 |
Issue number | 17 |
DOIs | |
Publication status | Published - 2010 Nov |
Externally published | Yes |
Keywords
- Compactification
- Dunce hat
- Symmetric hyperspace
- Symmetric product
ASJC Scopus subject areas
- Geometry and Topology