Theorems · Theorem · general topology
OpenPartialHomeomorph.image_source_inter_eq
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) (s : Set X), ↑e '' (e.source ∩ s) = e.target ∩ ↑e.symm ⁻¹' (e.source ∩ s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- OpenPartialHomeomorph.toPartialHomeomorphstatement and proof · cited by 851
- OpenPartialHomeomorph.toFun'statement · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- PartialEquiv.targetstatement · cited by 650
- OpenPartialHomeomorph.symmstatement · cited by 460
- PartialEquiv.image_source_inter_eqproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.IsImage.iff_symm_preimage_eq'proof · cited by 3
- OpenPartialHomeomorph.symm_image_target_inter_eqproof · cited by 1