Theorems · Theorem · general topology
TopologicalSpace.NoetherianSpace.exists_finset_irreducible
∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α] (s : TopologicalSpace.Closeds α),
∃ S, (∀ (k : ↥S), IsIrreducible ↑↑k) ∧ s = S.sup idIn a Noetherian space, every closed set is a finite union of irreducible closed sets.
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- SupSet.sSupproof · cited by 954
- Finset.supstatement · cited by 530
- TopologicalSpace.Closedsstatement and proof · cited by 168
- IsIrreduciblestatement and proof · cited by 59
- TopologicalSpace.NoetherianSpacestatement and proof · cited by 23
- Finset.sup_id_eq_sSupproof · cited by 12
- TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducibleproof · cited by 2
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