Theorems · Theorem · general topology
inter_mem_nhdsWithin
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : Set α) {t : Set α} {a : α}, t ∈ nhds a → s ∩ t ∈ nhdsWithin a s- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, 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
- self_mem_nhdsWithinproof · cited by 215
- Filter.inter_memproof · cited by 153
- Filter.mem_inf_of_leftproof · cited by 4
Cited by46
Results whose statement or proof uses this declaration.
- Ioo_mem_nhdsGTproof · cited by 20
- Ioo_mem_nhdsLTproof · cited by 19
- ContMDiffWithinAt.compproof · cited by 18
- MeasureTheory.locallyIntegrableOn_iffproof · cited by 5
- ContDiffWithinAt.contDiffOnproof · cited by 5
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_sdiffproof · cited by 4
- BoundedVariationOn.tendsto_eVariationOn_Ico_zeroproof · cited by 3
- continuousOn_extendFromproof · cited by 3
- continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWithproof · cited by 3
- HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_subproof · cited by 2
- HasFPowerSeriesWithinOnBall.continuousWithinAt_insertproof · cited by 2