SYMMETRIC PRODUCTS AS CONES, PEANO CURVES

摘要

For a continuum X, let F-n(X) be the hyperspace of all nonempty subsets of X with at most n-points. In this paper we prove that if X is a locally connected curve, then the following conditions are equivalent: (a) X is a cone, (b) F-n(X) is a cone for some n >= 2, and (c) F-n(X) is a cone for each n >= 2.