Volltext
May 12, 2006
Introduction to Compact Groups
Lemma A. Let A be an abelian group and F the set of finitely generated subgroups. Then (A,⊆) is a directed set such that A = T
F , and the compact dual group Ab is naturally isomorphic to the strict projective limit limF∈F Fb of the strict projective sys- tem
{F , Fb ∈ F;fF G:Gb → F , Fb ⊆ G in F } where fF G(χ) = χ|F for χ ∈ Gb.
Program for today.
Proof of the Duality Theorem: AB and CAB are naturally dual categories.
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