Theorems · Theorem · general topology
IsLocalHomeomorphOn.isDiscrete_image_iff
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X},
IsLocalHomeomorphOn f s → IsOpen s → (IsDiscrete (f '' s) ↔ IsDiscrete s)- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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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.imagestatement · cited by 5,609
- IsOpenstatement and proof · cited by 2,400
- IsDiscretestatement and proof · cited by 86
- IsLocalHomeomorphOnstatement and proof · cited by 22
- IsDiscrete.to_subtypeproof · cited by 8
- IsLocalHomeomorphOn.discreteTopology_image_iffproof · cited by 2
- IsLocalHomeomorphOn.isDiscrete_of_imageproof · cited by 1
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