Theorems · Theorem · general topology
OpenPartialHomeomorph.isOpen_inter_preimage
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) {s : Set Y}, IsOpen s → IsOpen (e.source ∩ ↑e ⁻¹' s)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, 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.preimagestatement · cited by 4,946
- IsOpenstatement and proof · cited by 2,400
- PartialEquiv.sourcestatement · cited by 964
- PartialHomeomorph.toPartialEquivstatement · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphstatement · cited by 851
- OpenPartialHomeomorph.toFun'statement · cited by 745
- OpenPartialHomeomorphstatement and proof · cited by 664
- OpenPartialHomeomorph.open_sourceproof · cited by 65
- ContinuousOn.isOpen_inter_preimageproof · cited by 13
- OpenPartialHomeomorph.continuousOnproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- ChartedSpace.discreteTopologyproof · cited by 1
- ChartedSpace.t1Spaceproof · cited by 1
- OpenPartialHomeomorph.IsImage.isOpen_iffproof · cited by 0
- IsLocalHomeomorph.isTopologicalBasisproof · cited by 0