Theorems · Theorem · general topology

AddCircle.liftIco_zero_continuous

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

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidFactArchimedeanTopologicalSpaceOrderTopologyTopologicalSpace