Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accessible values of Assouad and the lower dimensions of subsets   Let $E$ be a subset of a doubling metric space $(X,d)$. We prove that for any
$s\in [0, \dim_{A}E]$, where $\dim_{A}$ denotes the Assouad dimension, there
exists a subset $F$ of $E$ such that $\dim_{A}F=s$. We also show that the same
statement holds for the lower dimension $\dim_L$.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci