Theorems · Theorem · general topology
IsLocalHomeomorph.map_nhds_eq
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsLocalHomeomorph f → ∀ (x : X), Filter.map f (nhds x) = nhds (f x)- Defined in
- Mathlib.Topology.IsLocalHomeomorph
- Cited by
- 2 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Filter.mapstatement · cited by 819
- Set.mem_univproof · cited by 416
- IsLocalHomeomorphstatement and proof · cited by 35
- IsLocalHomeomorph.isLocalHomeomorphOnproof · cited by 6
- IsLocalHomeomorphOn.map_nhds_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalHomeomorph.isOpenMapproof · cited by 4
- Circle.hasBasis_centeredArc_div_two_powproof · cited by 1