Theorems · Theorem · general topology
TopologicalSpace.isSeparable_iUnion
∀ {α : Type u} [t : TopologicalSpace α] {ι : Sort u_2} [Countable ι] {s : ι → Set α},
TopologicalSpace.IsSeparable (⋃ i, s i) ↔ ∀ (i : ι), TopologicalSpace.IsSeparable (s i)- Defined in
- Mathlib.Topology.Bases
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCountable
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Cites8
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.iUnionstatement and proof · cited by 2,483
- Countablestatement and proof · cited by 633
- Set.subset_iUnionproof · cited by 81
- TopologicalSpace.IsSeparablestatement and proof · cited by 51
- TopologicalSpace.IsSeparable.monoproof · cited by 12
- TopologicalSpace.IsSeparable.iUnionproof · cited by 7
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