Original scientific paper
https://doi.org/10.21857/94kl4clkom
The (largest) Lebesgue number and its relative version
Vera Tonić
orcid.org/0000-0002-1427-7268
; Department of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
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.
Keywords
Lebesgue number; mesh of a cover; asymptotic dimension
Hrčak ID:
307499
URI
Publication date:
25.8.2023.
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