engleski

The (largest) Lebesgue number and its relative version

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 S. Buyalo - N. Lebedeva paper "Dimensions of locally and asymptotically self-similar spaces", 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.

the Lebesgue number, mesh of a cover, asymptotic dimension

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