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…
2 Citations
Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps
- Mathematics
- 2019
It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points…