Résumé:
The purpose of this paper is to introduce, by means of the extensions of almost closed
operators, the notion of almost closable linear operator acting in a Hilbert or Banach space. This
class of operators is strictly included in the class of all unbounded linear operators, it contains the
set of all closable operators and that of all almost closed operators and is invariant under finite
and countable sums, finite products, limits and integrals. We also present some fundamental
properties relative to almost closability and we define a locally convex Hausdorff topology in the
set of all almost closable operators.
