Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brouwer invariance theorems in reverse mathematics   In his book, John Stillwell wrote "finding the exact strength of the Brouwer
invariance theorems seems to me one of the most interesting open problems in
reverse mathematics." In this article, we solve Stillwell's problem by showing
that (some forms of) the Brouwer invariance theorems are equivalent to weak
K\"onig's lemma over the base system ${\sf RCA}_0$. In particular, there exists
an explicit algorithm which, whenever weak K\"onig's lemma is false, constructs
a topological embedding of $\mathbb{R}^4$ into $\mathbb{R}^3$.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas