Theorems · Definition · general topology

IsLocalHomeomorph.localInverseAt

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → {f : X → Y} → IsLocalHomeomorph f → X → OpenPartialHomeomorph Y X

A chosen local inverse for a local homeomorphism f at a point x.

Defined in: Mathlib.Topology.IsLocalHomeomorph
Cited by: 7 results in Mathlib
Foundations: Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
OpenPartialHomeomorphstatement · cited by 664
OpenPartialHomeomorph.symmproof · cited by 460
IsLocalHomeomorphstatement and proof · cited by 35

Cited by8

Results whose statement or proof uses this declaration.

IsLocalHomeomorph.localInverseAt_symmstatement · cited by 3
IsLocalHomeomorph.self_mem_localInverseAt_targetstatement · cited by 2
IsLocalHomeomorph.injOn_localInverseAt_targetstatement and proof · cited by 1
IsLocalHomeomorph.apply_localInverseAt_of_memstatement and proof · cited by 1
IsLocalHomeomorph.apply_self_mem_localInverseAt_sourcestatement and proof · cited by 1
IsLocalHomeomorph.localInverseAt_apply_selfstatement and proof · cited by 0
IsLocalHomeomorph.chartedSpaceOfRightInverseproof · cited by 0
IsLocalHomeomorph.localInverseAt.congr_simpstatement and proof · cited by 0