Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of universal differentiability sets   We prove that universal differentiability sets in Euclidean spaces possess
distinctive structural properties. Namely, we show that any universal
differentiability set contains a `kernel' in which the points of
differentiability of each Lipschitz function are dense. We further prove that
no universal differentiability set may be decomposed as a countable union of
relatively closed, non-universal differentiability sets. The sharpness of this
result, with respect to existing decomposibility results of the opposite
nature, is discussed.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci