Theorems · Theorem · general topology

AddCircle.liftIoc_continuous

∀ {𝕜 : Type u_1} {B : Type u_2} [inst : AddCommGroup 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : IsOrderedAddMonoid 𝕜]
  {p a : 𝕜} [hp : Fact (0 < p)] [inst_3 : Archimedean 𝕜] [inst_4 : TopologicalSpace 𝕜] [OrderTopology 𝕜]
  [inst_6 : TopologicalSpace B] {f : 𝕜 → B},
  f a = f (a + p) → ContinuousOn f (Set.Icc a (a + p)) → Continuous (AddCircle.liftIoc p a f)

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidFactArchimedeanTopologicalSpaceOrderTopologyTopologicalSpace