Theorems · Theorem · general topology
OpenPartialHomeomorph.isOpen_image_of_subset_source
∀ {X : Type u_1} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
(e : OpenPartialHomeomorph X Y) {s : Set X}, IsOpen s → s ⊆ e.source → IsOpen (↑e '' s)An open partial homeomorphism is an open map on its source: the image of an open subset of the source is open.
- Cited by
- 6 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.
Cites13
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
- IsOpenstatement and proof · cited by 2,400
- PartialEquiv.sourcestatement and proof · 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
- OpenPartialHomeomorph.open_targetproof · cited by 38
- ContinuousOn.isOpen_inter_preimageproof · cited by 13
- PartialHomeomorph.continuousOn_invFunproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- IsLocalHomeomorphOn.discreteTopology_image_iffproof · cited by 2
- IsClosedMap.isEvenlyCovered_of_openPartialHomeomorphproof · cited by 2
- NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOneproof · cited by 1
- OpenPartialHomeomorph.isOpen_image_source_interproof · cited by 1
- OpenPartialHomeomorph.isOpen_symm_image_iff_of_subset_targetproof · cited by 1
- OpenPartialHomeomorph.isOpen_image_symm_of_subset_targetproof · cited by 0