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Derived Projective Limits of Topological Abelian Groups

โœ Scribed by Fabienne Prosmans

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
246 KB
Volume
162
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

In this paper, we prove that the category TAb of topological Abelian groups is quasi-Abelian. Using results about derived projective limits in quasi-Abelian categories, we study exactness properties of the projective limit functor in TAb. If X is a projective system of TAb indexed by a filtering ordered set, we give a necessary and sufficient condition for the derived projective limit of X to be strict. We also characterize the countable projective systems of complete metrizable Abelian groups which are -acyclic in TAb.

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