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Theorems · Theorem · general topology

TopologicalSpace.IsSeparable.closure

∀ {α : Type u} [t : TopologicalSpace α] {s : Set α},
  TopologicalSpace.IsSeparable s → TopologicalSpace.IsSeparable (closure s)

Alias of the reverse direction of TopologicalSpace.isSeparable_closure.

Defined in
Mathlib.Topology.Bases
Cited by
10 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

stronglyMeasurable_of_tendsto · cited by 12stronglyMeasurable_of_ten…MeasureTheory.StronglyMeasurable.isSeparable_range · cited by 10StronglyMeasurable.isSepa…aestronglyMeasurable_of_tendsto_ae · cited by 9aestronglyMeasurable_of_t…ProbabilityTheory.IdentDistrib.integral_eq · cited by 4IdentDistrib.integral_eqstronglyMeasurable_deriv_with_param · cited by 3stronglyMeasurable_deriv_…ProbabilityTheory.IdentDistrib.aestronglyMeasurable_snd · cited by 3IdentDistrib.aestronglyMe…MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_id_map · cited by 2AEStronglyMeasurable.aest…stronglyMeasurable_derivWithin_Ici · cited by 2stronglyMeasurable_derivW…MeasureTheory.aestronglyMeasurable_id_of_isSeparable · cited by 1MeasureTheory.aestronglyM…isSeparable_range_derivWithin · cited by 1isSeparable_range_derivWi…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceclosure · cited by 1254closureTopologicalSpace.IsSeparable · cited by 51TopologicalSpace.IsSepara…TopologicalSpace.isSeparable_closure · cited by 1TopologicalSpace.isSepara…IsSeparable.closureCITED BYCITES

Cites5

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Cited by10

Results whose statement or proof uses this declaration.