Theorems · Theorem · general topology
TopologicalSpace.IsSeparable.mono
∀ {α : Type u} [t : TopologicalSpace α] {s u : Set α},
TopologicalSpace.IsSeparable s → u ⊆ s → TopologicalSpace.IsSeparable u- Defined in
- Mathlib.Topology.Bases
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 60 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
- LE.le.transproof · cited by 3,151
- closureproof · cited by 1,254
- Set.Countableproof · cited by 545
- TopologicalSpace.IsSeparablestatement and proof · cited by 51
Cited by12
Results whose statement or proof uses this declaration.
- stronglyMeasurable_of_tendstoproof · cited by 12
- aestronglyMeasurable_iff_aemeasurable_separableproof · cited by 10
- MeasureTheory.StronglyMeasurable.isSeparable_rangeproof · cited by 10
- TopologicalSpace.IsSeparable.of_separableSpaceproof · cited by 4
- stronglyMeasurable_deriv_with_paramproof · cited by 3
- stronglyMeasurable_derivWithin_Iciproof · cited by 2
- MeasureTheory.tendsto_integral_norm_approxOn_subproof · cited by 1
- MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonnegproof · cited by 1
- Convex.integral_memproof · cited by 1
- isSeparable_range_derivWithinproof · cited by 1
- TopologicalSpace.isSeparable_iUnionproof · cited by 0