Theorems · Theorem · general topology
IsOpenMap.map_nhdsSet_eq
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → Continuous f → ∀ (s : Set X), Filter.map f (nhdsSet s) = nhdsSet (f '' s)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Filterstatement · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- nhdsproof · cited by 5,554
- Continuousstatement and proof · cited by 2,592
- Set.iUnionproof · cited by 2,483
- iSupproof · cited by 2,415
- Filter.mapstatement and proof · cited by 819
- Continuous.continuousAtproof · cited by 297
- nhdsSetstatement and proof · cited by 267
- IsOpenMapstatement and proof · cited by 253
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.