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In the paper we introduce the concept of the Kuratowski distance between nonempty and bounded subsets of a Banach space. We show that the Kuratowski measure of noncompactness of a nonempty and bounded subset of a Banach space is equal to the Kuratowski distance of that subset to the family of all nonempty and relatively compact subsets of the mentioned Banach space.
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Banaś et al. (2026) studied this question.
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