Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On localizing topological algebras   Through the subsequent discussion we consider a certain particular sort of
(topological) algebras, which may substitute the `` structure sheaf algebras''
in many--in point of fact, in all--the situations of a geometrical character
that occur, thus far, in several mathematical disciplines, as for instance,
differential and/or algebraic geometry, complex (geometric) analysis etc. It is
proved that at the basis of this type of algebras lies the sheaf-theoretic
notion of (functional) localization, which, in the particular case of a given
topological algebra, refers to the respective ``Gel'fand transform algebra''
over the spectrum of the initial algebra. As a result, one further considers
the so-called ``geometric topological algebras'', having special cohomological
properties, in terms of their ``Gel'fand sheaves'', being also of a particular
significance for (abstract) differential-geometric applications; yet, the same
class of algebras is still ``closed'', with respect to appropriate inductive
limits, a fact which thus considerably broadens the sort of the topological
algebras involved, hence, as we shall see, their potential applications as
well.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
16
The categories of this paper are: stat