Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Close-to-regularity and completely regularity of bounded tri-linear maps   Let $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear map on
normed spaces. We say that $f$ is close-to-regular when $f^{t****s}=f^{s****t}$
and we say that $f$ is completely regular when all natural extensions are
equal. In this manuscript, we have some results on the close-to-regular maps
and investigate the close-to-regularity of tri-linear maps. We investigate the
relation between Arens regularity of bounded bilinear maps and
close-to-regularity bounded tri-linear maps. We give a simple criterion for the
completely regularity of tri-linear maps. We provide a necessary and sufficient
condition such that the fourth adjoint $D^{****}$ of a tri-derivation is again
a tri-derivation.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th