Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transversality of smooth definable maps in O-minimal structures   We present a definable smooth version of the Thom transversality theorem. We
show further that the set of non-transverse definable smooth maps is nowhere
dense in the definable smooth topology. Finally, we prove a definable version
of a theorem of Trotman which says that the Whitney $(a)$-regularity of a
stratification is necessary and sufficient for the stability of transversality.

15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org