Theorems · Theorem · general topology
TopologicalSpace.isSeparable_range
∀ {α : Type u} {β : Type u_1} [t : TopologicalSpace α] [inst : TopologicalSpace β] [TopologicalSpace.SeparableSpace α]
{f : α → β}, Continuous f → TopologicalSpace.IsSeparable (Set.range f)- Defined in
- Mathlib.Topology.Bases
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- Set.image_univproof · cited by 322
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- TopologicalSpace.IsSeparablestatement · cited by 51
- TopologicalSpace.isSeparable_univ_iffproof · cited by 4
- TopologicalSpace.IsSeparable.imageproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousOn.aestronglyMeasurableproof · cited by 21
- Continuous.stronglyMeasurableproof · cited by 7
- TopologicalSpace.IsSeparable.of_subtypeproof · cited by 3
- stronglyMeasurable_deriv_with_paramproof · cited by 3
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0