Theorems · Theorem · general topology

continuousAt_toIcoMod

∀ {𝕜 : Type u_1} [inst : AddCommGroup 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : IsOrderedAddMonoid 𝕜]
  [inst_3 : Archimedean 𝕜] [inst_4 : TopologicalSpace 𝕜] [OrderTopology 𝕜] {p : 𝕜} (hp : 0 < p) (a : 𝕜) {x : 𝕜},
  ¬x ≡ a [PMOD p] → ContinuousAt (toIcoMod hp a) x

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedeanTopologicalSpaceOrderTopology