Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Plurisubharmonic and holomorphic functions relative to the plurifine
  topology   A weak and a strong concept of plurifinely plurisubharmonic and plurifinely
holomorphic functions are introduced. Strong will imply weak. The weak concept
is studied further. A function f is weakly plurifinely plurisubharmonic if and
only if f o h is finely subharmonic for all complex affine-linear maps h. As a
consequence, the regularization in the plurifine topology of a pointwise
supremum of such functions is weakly plurifinely plurisubharmonic, and it
differs from the pointwise supremum at most on a pluripolar set. Weak plurifine
plurisubharmonicity and weak plurifine holomorphy are preserved under
composition with weakly plurifinely holomorphic maps.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci