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arXiv · 1409.2070

Uniform disconnectedness and Quasi-Assouad Dimension

Fan Lü·Li-Feng Xi
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Abstract

The uniform disconnectedness is an important invariant property under bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we introduce the quasi-Assouad dimension $\dim _{qA}$ such that $\dim _{qA}X<1$ implies its quasi uniform disconnectedness. We obtain $\overline{\dim } _{B}X\leq \dim _{qA}X\leq \dim _{A}X$ and compute the quasi-Assouad dimension of Moran set.

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Fan Lü, Li-Feng Xi. 2014-09-07. Uniform disconnectedness and Quasi-Assouad Dimension. https://arxiv.org/abs/1409.2070

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