Theorems · Theorem · general topology
IsLocalHomeomorphOn.isDiscrete_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 → IsDiscrete (f '' s) → IsDiscrete s- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Elemproof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- DiscreteTopologyproof · cited by 373
- IsDiscretestatement and proof · cited by 86
- IsLocalHomeomorphOnstatement and proof · cited by 22
- IsDiscrete.to_subtypeproof · cited by 8
- IsLocalHomeomorphOn.discreteTopology_of_imageproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalHomeomorphOn.isDiscrete_image_iffproof · cited by 0