Theorems · Theorem · general topology
mem_nhdsWithin_of_mem_nhds
∀ {α : Type u_1} [inst : TopologicalSpace α] {s t : Set α} {a : α}, s ∈ nhds a → s ∈ nhdsWithin a t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.mem_inf_of_leftproof · cited by 4
Cited by50
Results whose statement or proof uses this declaration.
- eventually_nhdsWithin_of_eventually_nhdsproof · cited by 17
- IsLindelof.elim_countable_subcoverproof · cited by 10
- contDiffOn_succ_iff_fderivWithinproof · cited by 8
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- StructureGroupoid.LocalInvariantProp.liftPropWithinAt_interproof · cited by 6
- ContMDiffWithinAt.add_sectionproof · cited by 4
- StructureGroupoid.LocalInvariantProp.congr_iffproof · cited by 4
- mdifferentiableWithinAt_add_sectionproof · cited by 4
- contDiffWithinAt_interproof · cited by 4
- MDifferentiableWithinAt.smul_sectionproof · cited by 3
- OpenPartialHomeomorph.nhdsWithin_source_interproof · cited by 3
- MeasureTheory.Measure.IsEverywherePos.of_forall_exists_nhds_eqproof · cited by 3