Theorems · Theorem · general topology
TopologicalSpace.NoetherianSpace.exists_isOpen_nonempty_subset_irreducibleComponent
∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α],
∀ Z ∈ irreducibleComponents α, ∃ o, IsOpen o ∧ o.Nonempty ∧ o ⊆ Z[Stacks Tag 0052](https://stacks.math.columbia.edu/tag/0052) ((3))
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- LE.le.transproof · cited by 3,151
- Compl.complproof · cited by 2,925
- Set.Nonemptystatement · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- Set.Finiteproof · cited by 1,814
- closureproof · cited by 1,254
- Eq.leproof · cited by 605
- Set.sUnionproof · cited by 392
- subset_closureproof · cited by 309
- isOpen_compl_iffproof · cited by 63
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