Theorems · Theorem · general topology
IsDiscrete.preimage
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
IsDiscrete s → ContinuousOn f (f ⁻¹' s) → Function.Injective f → IsDiscrete (f ⁻¹' s)- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterproof · cited by 8,121
- Set.preimagestatement and proof · cited by 4,946
- nhdsWithinproof · cited by 1,912
- ContinuousOnstatement and proof · cited by 1,411
- Filter.mapproof · cited by 819
- IsDiscretestatement and proof · cited by 86
- Set.mapsTo_preimageproof · cited by 35
- ContinuousOn.continuousWithinAtproof · cited by 26
- ContinuousWithinAt.tendsto_nhdsWithinproof · cited by 16
- Filter.map_pureproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singletonproof · cited by 1