Miroslav Bačák, Leonid Kovalev
Abstract: Let $X(n),$ for $n\in\mathbb{N},$ be the set of all subsets of a metric space
$(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped with the Hausdorff
metric is called a finite subset space. In this paper we are concerned with the
existence of Lipschitz retractions $r: X(n)\to X(n-1)$ for $n\ge2.$ It is known
that such retractions do not exist if $X$ is the one-dimensional sphere. On the
other hand L. Kovalev has recently established their existence in case $X$ is a
Hilbert space and he also posed a question as to whether or not such Lipschitz
retractions exist for $X$ being a Hadamard space. In the present paper we
answer this question in the positive.
ArXiv: 1603.01836