Theorems · Theorem · general topology
isMeagre_iUnion
∀ {X : Type u_1} {ι' : Sort u_4} [inst : TopologicalSpace X] [Countable ι'] {f : ι' → Set X},
(∀ (i : ι'), IsMeagre (f i)) → IsMeagre (⋃ i, f i)A countable union of meagre sets is meagre.
- Defined in
- Mathlib.Topology.GDelta.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCountable
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
- Set.iUnionstatement and proof · cited by 2,483
- Countablestatement and proof · cited by 633
- Set.compl_iUnionproof · cited by 32
- residualproof · cited by 23
- IsMeagrestatement and proof · cited by 18
- countable_iInter_memproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isMeagre_biUnionproof · cited by 1