Theorems · Theorem · general topology
Topology.IsInducing.map_nhds_eq
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace X],
Topology.IsInducing f → ∀ (x : X), Filter.map f (nhds x) = nhdsWithin (f x) (Set.range f)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.rangestatement · cited by 4,705
- nhdsWithinstatement · cited by 1,912
- Filter.mapstatement · cited by 819
- Topology.IsInducingstatement and proof · cited by 266
- Topology.IsInducing.eq_inducedproof · cited by 31
- map_nhds_induced_eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- map_nhds_subtype_valproof · cited by 6
- Topology.IsEmbedding.map_nhds_eqproof · cited by 2
- Topology.IsInducing.image_mem_nhdsWithinproof · cited by 0