Theory of spectral sequences. II

In this paper, we continue to discuss the theory of spectral sequences in Abelian categories. In this connection, attention is paid to the manifestation of different dualities in the theory of spectral sequences. The duality in locally convex, topological vector spaces is of special interest. We use results of functional analysis for solving (co)homology problems (theorems on nondegenerate pairing (co)homology) of manifolds. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 117–149, 2005.