Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly convex sets and modulus of nonconvexity   We consider a definition of a weakly convex set which is a generalization of
the notion of a weakly convex set in the sense of Vial and a proximally smooth
set in the sense of Clarke, from the case of the Hilbert space to a class of
Banach spaces with the modulus of convexity of the second order. Using the new
definition of the weakly convex set with the given modulus of nonconvexity we
prove a new retraction theorem and we obtain new results about continuity of
the intersection of two continuous set-valued mappings (one of which has
nonconvex images) and new affirmative solutions of the splitting problem for
selections. We also investigate relationship between the new definition and the
definition of a proximally smooth set and a smooth set.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol