Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed-point free maps of Euclidean spaces   Our main result states that every fixed-point free continuous self-map of
${\mathbb R}^{n}$ is colorable. This result can be re-formulated as follows: A
continuous map $f: {\mathbb R}^{n}\to {\mathbb R}^{n}$ is fixed-point free iff
$\widetilde f: \beta {\mathbb R}^{n}\to \beta {\mathbb R}^{n}$ is fixed-point
free. We also obtain a generalization of this fact and present some examples.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph