Theorems · Theorem · general topology

ContinuousAt.pathExtend

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {g : Y → ℝ} {l r : Y → X}
  (γ : (y : Y) → Path (l y) (r y)) {y : Y},
  ContinuousAt ↿γ (y, Set.projIcc 0 1 ⋯ (g y)) → ContinuousAt g y → ContinuousAt (fun i => (γ i).extend (g i)) y

Defined in

Mathlib.Topology.Path

Cited by

0 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace