Theorems · Theorem · general topology
closure_union
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, closure (s ∪ t) = closure s ∪ closure t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 64 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
- Compl.complproof · cited by 2,925
- closurestatement · cited by 1,254
- interiorproof · cited by 714
- Set.compl_unionproof · cited by 30
- Set.compl_interproof · cited by 26
- interior_interproof · cited by 22
- closure_eq_compl_interior_complproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.tendsto_approxOnproof · cited by 6
- frontier_inter_subsetproof · cited by 4
- tsupport_binop_subsetproof · cited by 3
- mulTSupport_binop_subsetproof · cited by 3
- CompactlySupportedContinuousMap.exists_add_of_leproof · cited by 2
- dense_coborderproof · cited by 1
- Topology.IsOpenEmbedding.baireSpaceproof · cited by 1
- subset_closure_inter_union_closure_compl_rightproof · cited by 0
- HasCompactMulSupport.infproof · cited by 0
- HasCompactSupport.infproof · cited by 0
- HasCompactSupport.supproof · cited by 0
- HasCompactMulSupport.supproof · cited by 0