Theorems · Theorem · general topology
nhdsWithin_eq_nhds
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s : Set α}, nhdsWithin a s = nhds a ↔ s ∈ nhds a- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- nhdsstatement · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.le_principal_iffproof · cited by 87
- inf_eq_leftproof · cited by 41
Cited by8
Results whose statement or proof uses this declaration.
- IsOpen.nhdsWithin_eqproof · cited by 15
- UniformContinuousOn.tendstoUniformlyproof · cited by 3
- curveIntegralFun_trans_of_lt_halfproof · cited by 2
- hasFDerivWithinAt_of_mem_nhdsproof · cited by 1
- MDifferentiableAt.isInteriorPoint_of_surjective_mfderivproof · cited by 1
- OpenPartialHomeomorph.map_extend_nhds_of_mem_interior_rangeproof · cited by 1
- oscillationWithin_nhds_eq_oscillationproof · cited by 1
- continuous_of_cover_nhdsproof · cited by 0