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arXiv · 2208.01427

The (largest) Lebesgue number and its relative version

Vera Tonić
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Abstract

In this paper we compare different definitions of the (largest) Lebesgue number of a cover $\mathcal{U}$ for a metric space $X$. We also introduce the relative version for the Lebesgue number of a covering family $\mathcal{U}$ for a subset $A\subseteq X$, 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 $\lambda$-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.

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Vera Tonić. 2022-08-02. The (largest) Lebesgue number and its relative version. https://arxiv.org/abs/2208.01427

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