Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complement of a $\sigma$-compact subset of a space with a $\pi$-tree
  also has a $\pi$-tree   We prove that the complement of a $\sigma$-compact subset of a topological
space that has a $\pi$-tree also has a $\pi$-tree. To do this, we construct the
foliage hybrid operation, which deals with foliage trees (that is,
set-theoretic trees with a `leaf' at each node). Then using this operation we
modify a $\pi$-tree of a space and get a $\pi$-tree for its subspace.

37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess