Analysis reveals Zaitov's metric enables perfect metrization for the hyperspace functor, suggesting significant properties in compact subset handling.
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 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.
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Kočinac et al. (2025) studied this question.
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