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*Axioms*, Volume 11, Issue 1 (January 2022) – 34 articles

**Cover Story**(view full-size image): We consider the Banach space consisting of real functions defined on a metric space which is locally compact and countable at infinity. Additionally, we assume that functions belonging to the space in question have increments tempered by a given modulus of continuity. The mentioned space is normed by a suitable norm connected with the given modulus of continuity. We investigate as an important particular case the Euclidean space Rk as the locally compact and countable at infinity metric space. Moreover, we also provide a few particular examples of spaces of such a type with moduli of continuity generated by the Lipschitz or Holder conditions. The main result of the paper presents a sufficient condition for relative compactness in the discussed Banach space consisting of real functions defined on the space Rk with increments tempered by an arbitrary modulus of continuity. View this paper.

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