THE SHEAVES REPRESENTATION OF HAUSDORFF SPECTRA.

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H-limit of Hausdorff spectrum of locally convex spaces with point of view using sheaves theory. Particular cases of regular H-limit are projective and inductive limits of separated lo- cally convex spaces. The class of H-spaces contains Fréchet spaces and is stable under the operations of forming countable inductive and pro- jective limits, closed subspaces and factor-spaces. Besides, for H-space the strengthened variant of the Closed Graph Theorem holds true. The space of germs of holomorphic functions on connected bounded subset will be provided with the topology (in general not separated) of uni- form convergence on the compact subsets and with the locally convex topology of the H-limit. We also present an essentially new approach to the study of sheaves based on the notion of Hausdorff spectra associated with the presheaf. [ABSTRACT FROM AUTHOR]