Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discontinuous non-linear mappings on locally convex direct limits   Consider the self-map F of the space of real-valued test functions on the
line which takes a test function f to the test function sending a real number x
to f(f(x))-f(0). We show that F is discontinuous, although its restriction to
the space of functions supported in K is smooth (and thus continuous), for each
compact subset K of the line. More generally, we construct mappings with
analogous pathological properties on spaces of compactly supported smooth
sections in vector bundles over non-compact bases. The results are useful in
infinite-dimensional Lie theory, where they can be used to analyze the precise
direct limit properties of test function groups and groups of compactly
supported diffeomorphisms.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics