Theorems · Theorem · general topology
isMeagre_biUnion
∀ {X : Type u_1} {ι : Type u_3} [inst : TopologicalSpace X] {I : Set ι},
I.Countable → ∀ {f : ι → Set X}, (∀ i ∈ I, IsMeagre (f i)) → IsMeagre (⋃ i ∈ I, f i)- Defined in
- Mathlib.Topology.GDelta.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 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.
Cites10
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.Elemproof · cited by 7,166
- Set.iUnionstatement and proof · cited by 2,483
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Set.iUnion_congr_Propproof · cited by 374
- Set.iUnion_coe_setproof · cited by 53
- IsMeagrestatement and proof · cited by 18
- isMeagre_iUnionproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- exists_of_not_isMeagre_biUnionproof · cited by 0