Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On dimensionally exotic maps   We call a value $y=f(x)$ of a map $f:X\to Y$ dimensionally regular if $\dim
X\le \dim(Y\times f^{-1}(y))$. It was shown in \cite{first-exotic} that if a
map $f:X\to Y$ between compact metric spaces does not have dimensionally
regular values, then $X$ is a Boltyanskii compactum, i.e. a compactum
satisfying the equality $\dim(X\times X)=2\dim X-1$. In this paper we prove
that every Boltyanskii compactum $X$ of dimension $\dim X \geq 6$ admits a map
$f:X\to Y$ without dimensionally regular values. Also we exhibit a
4-dimensional Boltyanskii compactum for which every map has a dimensionally
regular value.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs