Theorems · Theorem · general topology

ContinuousAt.IccExtend

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : LinearOrder α] {a b : α} {h : a ≤ b}
  [inst_1 : TopologicalSpace α] [OrderTopology α] [inst_3 : TopologicalSpace β] [inst_4 : TopologicalSpace γ] {x : γ}
  (f : γ → ↑(Set.Icc a b) → β) {g : γ → α},
  ContinuousAt ↿f (x, Set.projIcc a b h (g x)) →
    ContinuousAt g x → ContinuousAt (fun a_1 => Set.IccExtend h (f a_1) (g a_1)) x

Defined in

Mathlib.Topology.Order.ProjIcc

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyTopologicalSpaceTopologicalSpace