Theorems · Theorem · general topology
nhdsWithin_inter_of_mem
∀ {α : Type u_1} [inst : TopologicalSpace α] {a : α} {s t : Set α},
s ∈ nhdsWithin a t → nhdsWithin a (s ∩ t) = nhdsWithin a t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 71 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 and proof · cited by 8,121
- nhdsWithinstatement and proof · cited by 1,912
- inf_eq_rightproof · cited by 64
- nhdsWithin_le_of_memproof · cited by 8
- nhdsWithin_interproof · cited by 6
Cited by20
Results whose statement or proof uses this declaration.
- nhdsWithin_Ioo_eq_nhdsGTproof · cited by 9
- nhdsWithin_inter_of_mem'proof · cited by 8
- nhdsWithin_Ioo_eq_nhdsLTproof · cited by 7
- MeasureTheory.locallyIntegrableOn_iffproof · cited by 5
- nhdsWithin_Icc_eq_nhdsGEproof · cited by 5
- Topology.IsInducing.locallyCompactSpaceproof · cited by 4
- OpenPartialHomeomorph.map_extend_nhdsWithin_eq_imageproof · cited by 3
- OpenPartialHomeomorph.nhdsWithin_source_interproof · cited by 3
- nhdsWithin_Ioc_eq_nhdsGTproof · cited by 3
- Ne.nhdsWithin_sdiff_singletonproof · cited by 2
- Convex.nhdsWithin_inter_Iio_eq_nhdsLTproof · cited by 2
- Convex.nhdsWithin_inter_Ioi_eq_nhdsGTproof · cited by 2