Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 231-243.

THE (LARGEST) LEBESGUE NUMBER AND ITS RELATIVE VERSION/h3>

Vera Tonić

Abstract.   In this paper we compare different definitions of the (largest) Lebesgue number of a cover U for a metric space X. We also introduce the relative version for the Lebesgue number of a covering family U for a subset A ⊆ X, and justify the relevance of introducing it by giving a corrected statement and proof of the Lemma 3.4 from the paper by Buyalo and Lebedeva (2007), involving λ-quasi homothetic maps with coefficient R between metric spaces and the comparison of the mesh and the Lebesgue number of a covering family for a subset on both sides of the map.

2020 Mathematics Subject Classification.   54E35, 51F30.

Key words and phrases.   Lebesgue number, mesh of a cover, asymptotic dimension.

DOI: https://doi.org/10.21857/94kl4clkom

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