In this paper we investigate the Lipschitz equivalence of dust-like self-similar sets in ℝd. One of the fundamental results by Falconer and Marsh [On the Lipschitz equivalence of Cantor sets, Mathematika, 39 (1992), 223-233] establishes conditions for Lipschitz equivalence based on the algebraic properties of the contraction ratios of the self-similar sets. In this paper we extend the study by examining deeper such connections. A key ingredient of our study is the introduction of a new equivalent relation between two dust-like self-similar set...
