• Corpus ID: 46732356

The Pontryagin duals of Q / Z and Q

@inproceedings{Bell2015ThePD,
  title={The Pontryagin duals of Q / Z and Q},
  author={Jordan Bell},
  year={2015}
}
Write S = {z ∈ C : |z| = 1}. A character of a locally compact abelian group G is a continuous group homomorphism G → S. We denote by Ĝ the set of characters of G, where for φ1, φ2 ∈ Ĝ and x ∈ G, we define (φ1φ2)(x) = φ1(x)φ2(x). We assign Ĝ the final topology for the family of functions {φ 7→ φ(x) : x ∈ G}, i.e., the coarsest topology on Ĝ so that for each x ∈ G, the function φ 7→ φ(x) is continuous Ĝ→ S. With this topology, it is a fact that Ĝ is itself a locally compact abelian group, called… 
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