Theorems · Theorem · general topology
PartialHomeomorph.image_source_inter_eq
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (e : PartialHomeomorph X Y)
(s : Set X), ↑e '' (e.source ∩ s) = e.target ∩ ↑e.symm ⁻¹' (e.source ∩ s)- Defined in
- Mathlib.Topology.PartialHomeomorph.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement and proof · cited by 917
- PartialEquiv.targetstatement · cited by 650
- PartialHomeomorphstatement and proof · cited by 73
- PartialHomeomorph.toFun'statement · cited by 57
- PartialHomeomorph.symmstatement · cited by 38
- PartialEquiv.image_source_inter_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- PartialHomeomorph.symm_image_target_inter_eqproof · cited by 0