Theorems · Theorem · general topology
TopologicalSpace.isSeparable_univ_iff
∀ {α : Type u} [t : TopologicalSpace α], TopologicalSpace.IsSeparable Set.univ ↔ TopologicalSpace.SeparableSpace α- Defined in
- Mathlib.Topology.Bases
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 67 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- TopologicalSpace.SeparableSpacestatement · cited by 109
- TopologicalSpace.IsSeparablestatement · cited by 51
- dense_univproof · cited by 12
- Dense.isSeparable_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.isSeparable_rangeproof · cited by 5
- TopologicalSpace.IsSeparable.of_separableSpaceproof · cited by 4
- ContinuousOn.isSeparable_imageproof · cited by 1
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0