Theorems · Theorem · general topology
mem_nhdsWithin
∀ {α : Type u_1} [inst : TopologicalSpace α] {t : Set α} {a : α} {s : Set α},
t ∈ nhdsWithin a s ↔ ∃ u, IsOpen u ∧ a ∈ u ∧ u ∩ s ⊆ t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 70 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.
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
- IsOpenstatement · cited by 2,400
- nhdsWithinstatement and proof · cited by 1,912
- Filter.HasBasis.mem_iffproof · cited by 193
- nhdsWithin_basis_openproof · cited by 6
Cited by29
Results whose statement or proof uses this declaration.
- differentiableWithinAt_localInvariantPropproof · cited by 13
- ContDiffOn.ftaylorSeriesWithinproof · cited by 11
- nhdsWithin_insert_of_neproof · cited by 9
- contDiffOn_succ_iff_fderivWithinproof · cited by 8
- ContDiffWithinAt.contDiffOn'proof · cited by 7
- iteratedFDerivWithin_add_applyproof · cited by 5
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- MeromorphicOn.congr_codiscreteWithinproof · cited by 3
- nhdsNE_of_nhdsNE_sdiff_finiteproof · cited by 3
- IsOpen.isEverywherePosproof · cited by 2
- ContMDiffWithinAt.contMDiffOn'proof · cited by 2
- integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2