Theorems · Theorem · general topology
Set.Finite.closure_biUnion
∀ {X : Type u} [inst : TopologicalSpace X] {ι : Type u_1} {s : Set ι},
s.Finite → ∀ (f : ι → Set X), closure (⋃ i ∈ s, f i) = ⋃ i ∈ s, closure (f i)- Defined in
- Mathlib.Topology.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 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.
Cites13
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
- Compl.complproof · cited by 2,925
- Set.iUnionstatement and proof · cited by 2,483
- Set.Finitestatement and proof · cited by 1,814
- closurestatement · cited by 1,254
- Set.iInterproof · cited by 1,084
- interiorproof · cited by 714
- Set.iUnion_congr_Propproof · cited by 374
- Set.compl_iUnionproof · cited by 32
- Set.compl_iInterproof · cited by 31
- closure_eq_compl_interior_complproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.closure_sUnionproof · cited by 1
- closure_iUnion₂_le_natproof · cited by 1
- closure_iUnion₂_lt_natproof · cited by 0
- Finset.closure_biUnionproof · cited by 0