We characterize all Fréchet quotients of the space 𝒜(Ω) of (complex-valued) real-analytic functions on an arbitrary open set $Ω ⊆ ℝ^{d}$. We also characterize those Fréchet spaces E such that every short exact sequence of the form 0 → E → X → 𝒜(Ω) → 0 splits.
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We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
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