Theorems · Theorem · general topology
TopologicalSpace.IsSeparable.union
∀ {α : Type u} [t : TopologicalSpace α] {s u : Set α},
TopologicalSpace.IsSeparable s → TopologicalSpace.IsSeparable u → TopologicalSpace.IsSeparable (s ∪ u)- Defined in
- Mathlib.Topology.Bases
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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.
Cites4
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
- TopologicalSpace.IsSeparablestatement and proof · cited by 51
- TopologicalSpace.isSeparable_unionproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyMeasurable.separableSpace_range_union_singletonproof · cited by 11
- MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonnegproof · cited by 1
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0