  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.
