Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restrictions of smooth functions to a closed subset   We first provide an approach to the recent conjecture of
Bierstone-Milman-Pawlucki on Whitney's old problem on smooth extendability of
functions defined on a closed subset of a Euclidean space, using higher order
paratangent bundle they introduced. For example, the conjecture is affirmative
for classical fractal sets. Next, we give a sharpened form of Spallek's theorem
on controllability of flatness by the values on a closed set. The
multi-dimensional Vandermonde matrix plays an important role in both cases.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
19
The categories of this paper are: eess