Theorems · Theorem · general topology

IsLocalHomeomorph.apply_localInverseAt_of_mem

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
  (hf : IsLocalHomeomorph f) {x : X} {y : Y}, y ∈ (hf.localInverseAt x).source → f (↑(hf.localInverseAt x) y) = y

If y lies in the source of localInverseAt x, then f (localInverseAt x y) = y.

Defined in

Mathlib.Topology.IsLocalHomeomorph

Cited by

1 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace