Theorems · Theorem · global analysis
ModelWithCorners.map_nhds_eq
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (x : H),
Filter.map (↑I) (nhds x) = nhdsWithin (↑I x) (Set.range ↑I)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterstatement · cited by 8,121
- nhdsstatement · cited by 5,554
- Set.rangestatement · cited by 4,705
- ModelWithCornersstatement and proof · cited by 2,462
- nhdsWithinstatement · cited by 1,912
- Filter.mapstatement · cited by 819
- ModelWithCorners.toFun'statement · cited by 373
- Topology.IsClosedEmbedding.isEmbeddingproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.map_extend_nhdsproof · cited by 6
- ModelWithCorners.image_mem_nhdsWithinproof · cited by 2
- ModelWithCorners.symm_map_nhdsWithin_rangeproof · cited by 1