Theorems · Theorem · general topology

eventuallyEq_toIocDiv_nhdsLE

∀ {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 x : 𝕜),
  toIocDiv hp a =ᶠ[nhdsWithin x (Set.Iic x)] fun x_1 => toIocDiv hp a x

toIocDiv is eventually constant on the left at every point.

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

2 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedeanTopologicalSpaceOrderTopology