Theorems · Theorem · general topology
mem_nhdsWithin_iff_exists_mem_nhds_inter
∀ {α : Type u_1} [inst : TopologicalSpace α] {t : Set α} {a : α} {s : Set α},
t ∈ nhdsWithin a s ↔ ∃ u ∈ nhds a, u ∩ s ⊆ t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 69 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.
Cites8
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.HasBasis.mem_iffproof · cited by 193
- Filter.basis_setsproof · cited by 105
- nhdsWithin_hasBasisproof · cited by 15
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_sdiffproof · cited by 4
- preimage_extChartAt_eventuallyEq_compl_singletonproof · cited by 3
- TFAE_mem_nhdsGTproof · cited by 3
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- IsCompact.elim_nhdsWithin_subcover'proof · cited by 1
- Function.locallyFinsuppWithin.disjoint_nhdsWithin_cofinite_of_memproof · cited by 1
- Complex.differentiableOn_update_limUnder_of_bddAboveproof · cited by 1
- nhds_of_nhdsWithin_of_nhdsproof · cited by 0
- IsCompact.elim_nhdsWithin_subcoverproof · cited by 0
- MeasureTheory.Filtration.rightCont_selfproof · cited by 0
- MeasureTheory.Measure.isEverywherePos_everywherePosSubsetproof · cited by 0