Tightness and Distinguished Fréchet Spaces

Abstract

In this chapter, we apply the concept of tightness to study distinguished Fréchet spaces. We show that a Fréchet space is distinguished if and only if its strong dual has countable tightness. This approach to studying distinguished Fréchet spaces leads to a rich supply of (DF)-spaces whose weak ^∗ duals are quasi-Suslin but not K-analytic. The small cardinals $\mathfrak{b}$ and $\mathfrak{d}$ will be used to improve the analysis of Köthe’s echelon nondistinguished Fréchet space λ ₁(A).