Theorems · Theorem · general topology
nhdsSet_union
∀ {X : Type u_2} [inst : TopologicalSpace X] (s t : Set X), nhdsSet (s ∪ t) = nhdsSet s ⊔ nhdsSet t- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 51 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.
Cites9
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
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- SupSet.sSupproof · cited by 954
- nhdsSetstatement · cited by 267
- Set.image_unionproof · cited by 48
- sSup_unionproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- nhdsSet_insertproof · cited by 4
- UpperHemicontinuousWithinAt.unionproof · cited by 2
- SeparatedNhds.union_leftproof · cited by 2
- Filter.Eventually.union_nhdsSetproof · cited by 1
- IsCompact.mem_nhdsSet_prod_of_forallproof · cited by 1
- IsClosed.nhdsSet_le_supproof · cited by 1
- union_mem_nhdsSetproof · cited by 1
- nhdsKer_unionproof · cited by 0