Lipschitz retraction of finite subsets of Hilbert spaces
  Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset\dots$. We prove that this sequence admits Lipschitz retractions $X(n)\to X(n-1)$ when $X$ is a Hilbert space. 
Leonid V. Kovalev
math.MG