On perfectness of Zaitov metrization of the hyperspace functor

Abstract

Recently, A.~Zaitov suggested a new metric on the space of all
nonempty compact subsets of a given metric space. In the present
paper we show that this metric turns the hyperspace functor {\sf
exp} into a perfect metrizable functor. Further, we establish that
the hyperspace functor has many remarkable properties with respect
to this metrization. In particular, this functor preserves isometric
embeddings.