Theorems · Theorem · general topology

Set.LeftInvOn.map_nhdsWithin_eq

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {g : β → α}
  {x : β} {s : Set β},
  Set.LeftInvOn f g s →
    f (g x) = x →
      ContinuousWithinAt f (g '' s) (g x) →
        ContinuousWithinAt g s x → Filter.map g (nhdsWithin x s) = nhdsWithin (g x) (g '' s)

Defined in

Mathlib.Topology.ContinuousOn

Cited by

3 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace