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1997 | 123 | 3 | 275-290
Tytuł artykułu

Standard exact projective resolutions relative to a countable class of Fréchet spaces

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We will show that for each sequence of quasinormable Fréchet spaces $(E_n)_ℕ$ there is a Köthe space λ such that $Ext^1(λ(A), λ(A) = Ext^1 (λ(A), E_n)=0$ and there are exact sequences of the form $... → λ(A) → λ(A) → λ(A) → λ(A) → {E_n} → 0$. If, for a fixed ℕ, $E_n$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 → λ(A) → λ(A) → {E_n} → 0$. The result has some applications in the theory of the functor $Ext^1$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  • Fachbereich Physikalische Technik, Märkische Fachhochschule Iserlohn, Frauenstuhlweg 31, D-58644 Iserlohn, Germany
  • Bergische Universität, Gesamthochschule Wuppertal, FB Mathematik, Gaussstr. 20, D-42097 Wuppertal, Germany
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