Abstract
We investigate two Lipschitz invariants of metric spaces defined by δ-connected components, called the maximal power law property and the perfectly disconnectedness. The first property has been studied in literature for some self-similar sets and Bedford-McMullen carpets, while the second property seems to be new. For a self-affine Sierpiński sponge E, we first show that E satisfies the maximal power law if and only if E and all its major projections contain trivial connected components; secondly, we show that E is perfectly disconnected if and only if E and all its major projections are totally disconnected.
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