Bibliography: pages 102-106.A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who derived almost all the important results concerning such spaces. The "generalized DF spaces" in the title of this thesis are locally convex topological vector spaces whose topologies are determined by their restrictions to an absorbent sequence of bounded sets. In the case when this sequence is a fundamental sequence of bounded sets, we obtain the gDF spaces. Many. of the properties of DF spaces are shared by all gDF spaces
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