Theorems · Theorem · general topology
TopologicalSpace.noetherianSpace_set_iff
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : Set α), TopologicalSpace.NoetherianSpace ↑s ↔ ∀ t ⊆ s, IsCompact t- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites7
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.Elemstatement and proof · cited by 7,166
- IsCompactstatement and proof · cited by 1,282
- Topology.IsEmbedding.subtypeValproof · cited by 41
- TopologicalSpace.NoetherianSpacestatement · cited by 23
- Topology.IsEmbedding.isCompact_iffproof · cited by 17
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