Theorems · Theorem · general topology

IsLocalHomeomorph.injOn_localInverseAt_target

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
  (hf : IsLocalHomeomorph f) {x : X}, Set.InjOn f (hf.localInverseAt x).target

The function f is injective on the target of localInverseAt x.

Defined in

Mathlib.Topology.IsLocalHomeomorph

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace