Theorems · Theorem · general topology
map_nhds_subtype_val
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} (x : ↑s), Filter.map Subtype.val (nhds x) = nhdsWithin (↑x) s- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 8,121
- Set.Elemstatement and proof · cited by 7,166
- nhdsstatement · cited by 5,554
- nhdsWithinstatement and proof · cited by 1,912
- Filter.mapstatement · cited by 819
- Topology.IsInducing.subtypeValproof · cited by 43
- Subtype.range_valproof · cited by 41
- Topology.IsInducing.map_nhds_eqproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- nhdsWithin_eq_map_subtype_coeproof · cited by 5
- preimage_nhdsWithin_coinduced'proof · cited by 2
- preimage_coe_mem_nhds_subtypeproof · cited by 2
- OpenPartialHomeomorph.nhds_eq_comap_inf_principalproof · cited by 1
- IsOpen.smul_sphereproof · cited by 0
- mem_nhds_subtype_iff_nhdsWithinproof · cited by 0