Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On continuous choice of retractions onto nonconvex subsets   For a Banach space $B$ and for a class $\A$ of its bounded closed retracts,
endowed with the Hausdorff metric, we prove that retractions on elements $A \in
\A$ can be chosen to depend continuously on $A$, whenever nonconvexity of each
$A \in \A$ is less than $\f{1}{2}$. The key geometric argument is that the set
of all uniform retractions onto an $\a-$paraconvex set (in the spirit of E.
Michael) is $\frac{\a}{1-\a}-$paraconvex subset in the space of continuous
mappings of $B$ into itself. For a Hilbert space $H$ the estimate
$\frac{\a}{1-\a}$ can be improved to $\frac{\a (1+\a^{2})}{1-\a^{2}}$ and the
constant $\f{1}{2}$ can be reduced to the root of the equation $\a+
\a^{2}+a^{3}=1$.

17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an