DF-space
In the field of functional analysis, DF-spaces, also written (DF)-spaces are locally convex topological vector space having a property that is shared by locally convex metrizable topological vector spaces. They play a considerable part in the theory of topological tensor products.[1]
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DF-spaces were first defined by Alexander Grothendieck and studied in detail by him in (Grothendieck 1954). Grothendieck was led to introduce these spaces by the following property of strong duals of metrizable spaces: If is a metrizable locally convex space and is a sequence of convex 0-neighborhoods in such that absorbs every strongly bounded set, then is a 0-neighborhood in (where is the continuous dual space of endowed with the strong dual topology).[2]