Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relations between topological and metrical properties of self-affine
  Sierpi$\acute{\text{n}}$ski sponges   We investigate two Lipschitz invariants of metric spaces defined by
$\delta$-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 Sierpi$\acute{\text{n}}$ski 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.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex