Theorems · Theorem · general topology
Set.Finite.isSeparable
∀ {α : Type u} [t : TopologicalSpace α] {s : Set α}, s.Finite → TopologicalSpace.IsSeparable s- Defined in
- Mathlib.Topology.Bases
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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.Finitestatement and proof · cited by 1,814
- TopologicalSpace.IsSeparablestatement · cited by 51
- Set.Finite.countableproof · cited by 30
- Set.Countable.isSeparableproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyMeasurable.separableSpace_range_union_singletonproof · cited by 11
- MeasureTheory.StronglyMeasurable.isSeparable_rangeproof · cited by 10
- MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonnegproof · cited by 1
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0