Theorems · Theorem · general topology

AddCircle.coe_image_Ico_eq

∀ {𝕜 : Type u_1} [inst : AddCommGroup 𝕜] (p : 𝕜) [inst_1 : LinearOrder 𝕜] [IsOrderedAddMonoid 𝕜] [hp : Fact (0 < p)]
  (a : 𝕜) [Archimedean 𝕜], QuotientAddGroup.mk '' Set.Ico a (a + p) = Set.univ

The image of the closed-open interval [a, a + p) under the quotient map 𝕜 → AddCircle p is the entire space.

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

3 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidFactArchimedean