Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finitness theorem for Multi-K-Bi-Lipschtiz equivalence of map-germs   Let $P^{k}(n,p) $ be the set of all real polynomial map germs $f = ( f_1 ,
..., f_p ) : (\mathbb{R}^{n},0) \rightarrow (\mathbb{R}^{p},0)$ with degree of
$f_1 , ...,f_p$ less than or equal to $ k \in \mathbb{N}$. The main result of
this paper shows that the set of equivalence classes of $ P^{k}(n,p)$, with
respect to multi-$\mathcal{K}$-bi-Lipschitz equivalence, is finite.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg