Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.separableSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α],
TopologicalSpace.SeparableSpace (TopologicalSpace.NonemptyCompacts α) ↔ TopologicalSpace.SeparableSpace α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Bot.botproof · cited by 4,720
- TopologicalSpace.Compactsproof · cited by 386
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- TopologicalSpace.SeparableSpacestatement and proof · cited by 109
- Set.finite_singletonproof · cited by 70
- Set.union_compl_selfproof · cited by 57
- TopologicalSpace.IsSeparableproof · cited by 51
- TopologicalSpace.NonemptyCompacts.continuous_toCompactsproof · cited by 8
- TopologicalSpace.NonemptyCompacts.range_toCompactsproof · cited by 5
- TopologicalSpace.isSeparable_rangeproof · cited by 5
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