Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the closedness of the sum of n subspaces of a Hilbert space   We give necessary and sufficient conditions for the sum of n subspaces of a
Hilbert space to be closed. We also present various properties of n-tuples of
subspaces with closed sum.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph