Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-removability of Sierpinski carpets   We prove that all Sierpi\'nski carpets in the plane are non-removable for
(quasi)conformal maps. More precisely, we show that for any two Sierpi\'nski
carpets $S,S'\subset \hat{\mathbb{C}}$ there exists a homeomorphism $f\colon
\hat{\mathbb{C}}\to \hat{\mathbb{C}}$ that is conformal in
$\hat{\mathbb{C}}\setminus S$ and it maps $S$ onto $S'$. The proof is
topological and it utilizes the ideas of the topological characterization of
Whyburn. As a corollary, we obtain a partial answer to a question of Bishop,
whether any planar continuum with empty interior and positive measure can be
mapped to a set of measure zero with an exceptional homeomorphism of the plane,
conformal off that set.

4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph