Theorems · Theorem · general topology

AddCircle.continuousAt_equivIoc

∀ {𝕜 : Type u_1} [inst : AddCommGroup 𝕜] (p : 𝕜) [inst_1 : LinearOrder 𝕜] [inst_2 : IsOrderedAddMonoid 𝕜]
  [hp : Fact (0 < p)] (a : 𝕜) [inst_3 : Archimedean 𝕜] [inst_4 : TopologicalSpace 𝕜] [OrderTopology 𝕜]
  {x : AddCircle p}, x ≠ ↑a → ContinuousAt (⇑(AddCircle.equivIoc p a)) x

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidFactArchimedeanTopologicalSpaceOrderTopology