Theorems · Definition · Lie groups
PontryaginDual
(A : Type u_1) → [Monoid A] → [TopologicalSpace A] → Type (max u_1 0)
The Pontryagin dual of A is the group of continuous homomorphism A → Circle.
- Defined in
- Mathlib.Topology.Algebra.PontryaginDual
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Monoidstatement and proof · cited by 3,887
- Circleproof · cited by 227
- ContinuousMonoidHomproof · cited by 104
Cited by9
Results whose statement or proof uses this declaration.
- PontryaginDual.mapstatement · cited by 4
- PontryaginDual.extstatement and proof · cited by 4
- PontryaginDual.mapHomstatement · cited by 0
- PontryaginDual.map_applystatement and proof · cited by 0
- PontryaginDual.map_compstatement and proof · cited by 0
- PontryaginDual.map_mulstatement and proof · cited by 0
- PontryaginDual.map_onestatement and proof · cited by 0
- PontryaginDual.one_applystatement · cited by 0
- PontryaginDual.ext_iffstatement and proof · cited by 0