Theorems · Theorem · general topology
IsLocalHomeomorphOn.discreteTopology_of_image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X},
IsLocalHomeomorphOn f s → ∀ [DiscreteTopology ↑(f '' s)], DiscreteTopology ↑s- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 3 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.
Cites23
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.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Set.preimageproof · cited by 4,946
- IsOpenproof · cited by 2,400
- PartialEquiv.sourceproof · cited by 964
- PartialHomeomorph.toPartialEquivproof · cited by 917
- OpenPartialHomeomorph.toPartialHomeomorphproof · cited by 851
- OpenPartialHomeomorph.toFun'proof · cited by 745
- OpenPartialHomeomorphproof · cited by 664
- DiscreteTopologystatement and proof · cited by 373
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalHomeomorphOn.discreteTopology_image_iffproof · cited by 2
- IsLocalHomeomorphOn.isDiscrete_of_imageproof · cited by 1
- IsLocalHomeomorph.comap_discreteTopologyproof · cited by 0