Theorems · Theorem · general topology
nhdsSet_insert
∀ {X : Type u_2} [inst : TopologicalSpace X] (x : X) (s : Set X), nhdsSet (insert x s) = nhds x ⊔ nhdsSet s- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 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 and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- nhdsSetstatement and proof · cited by 267
- Set.insert_eqproof · cited by 47
- nhdsSet_singletonproof · cited by 19
- nhdsSet_unionproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- nhdsSet_Iocproof · cited by 1
- nhdsSet_Iciproof · cited by 1
- nhdsSet_Iccproof · cited by 0
- nhdsSet_Icoproof · cited by 0