Theorems · Theorem · general topology
TopologicalSpace.IsSeparable.iUnion
∀ {α : Type u} [t : TopologicalSpace α] {ι : Sort u_2} [Countable ι] {s : ι → Set α},
(∀ (i : ι), TopologicalSpace.IsSeparable (s i)) → TopologicalSpace.IsSeparable (⋃ i, s i)- Defined in
- Mathlib.Topology.Bases
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 74 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.
Cites12
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
- LE.le.transproof · cited by 3,151
- Set.iUnionstatement and proof · cited by 2,483
- closureproof · cited by 1,254
- Countablestatement and proof · cited by 633
- Set.Countableproof · cited by 545
- closure_monoproof · cited by 133
- Set.subset_iUnionproof · cited by 81
- TopologicalSpace.IsSeparablestatement and proof · cited by 51
- Set.countable_iUnionproof · cited by 22
- Set.iUnion_subset_iffproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- stronglyMeasurable_of_tendstoproof · cited by 12
- MeasureTheory.StronglyMeasurable.isSeparable_rangeproof · cited by 10
- aestronglyMeasurable_of_tendsto_aeproof · cited by 9
- TopologicalSpace.IsSeparable.spanproof · cited by 3
- MeasureTheory.AEStronglyMeasurable.sum_measureproof · cited by 2
- TopologicalSpace.isSeparable_iUnionproof · cited by 0