Theorems · Theorem · general topology
nhdsWithin_inter
∀ {α : Type u_1} [inst : TopologicalSpace α] (a : α) (s t : Set α),
nhdsWithin a (s ∩ t) = nhdsWithin a s ⊓ nhdsWithin a t- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- nhdsproof · cited by 5,554
- nhdsWithinstatement · cited by 1,912
- Filter.principalproof · cited by 740
- inf_assocproof · cited by 53
- inf_idemproof · cited by 37
- Filter.inf_principalproof · cited by 29
- inf_left_commproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- nhdsWithin_inter_of_memproof · cited by 20
- OpenPartialHomeomorph.map_extend_nhdsWithinproof · cited by 6
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- MonotoneOn.countable_not_continuousWithinAt_Ioiproof · cited by 2
- mdifferentiableWithinAt_iff_target_interproof · cited by 0
- uniqueMDiffWithinAt_iffproof · cited by 0