Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brouwer fixed point theorem and the Borsuk--Ulam theorem   These informal notes, not intended for publication, provide an approach to
the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's
proof of the Brouwer fixed point theorem. They are intended to be accessible to
anyone with a knowledge of basic point-set topology and several variable
calculus. Some of the argument relies upon previous ideas of Shchepin.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga