Theorems · Theorem · general topology
union_mem_nhdsSet
∀ {X : Type u_2} [inst : TopologicalSpace X] {s₁ s₂ t₁ t₂ : Set X},
s₁ ∈ nhdsSet t₁ → s₂ ∈ nhdsSet t₂ → s₁ ∪ s₂ ∈ nhdsSet (t₁ ∪ t₂)- Defined in
- Mathlib.Topology.NhdsSet
- Cited by
- 1 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.
Cites6
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
- nhdsSetstatement and proof · cited by 267
- Filter.union_mem_supproof · cited by 9
- nhdsSet_unionproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsCompact.exists_thickening_image_subsetproof · cited by 0