Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrical characterization of semilinear isomorphisms of vector spaces
  and semilinear homeomorphisms of normed spaces   Let $V$ and $V'$ be vector spaces over division rings (possible
infinite-dimensional) and let ${\mathcal P}(V)$ and ${\mathcal P}(V')$ be the
associated projective spaces. We say that $f:{\mathcal P}(V)\to {\mathcal
P}(V')$ is a PGL-{\it mapping} if for every $h\in {\rm PGL}(V)$ there exists
$h'\in {\rm PGL}(V')$ such that $fh=h'f$. We show that for every PGL-bijection
the inverse mapping is a semicollineation. Also, we obtain an analogue of this
result for the projective spaces associated to normed spaces.

35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin