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Stable inverse-limit sequences, with application to Fréchet algebras. (English) Zbl 0874.46048

Summary: The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of Abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.

MSC:

46M40 Inductive and projective limits in functional analysis
46H05 General theory of topological algebras
46J05 General theory of commutative topological algebras
46M15 Categories, functors in functional analysis
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
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