Theorems · Theorem · general topology
TopologicalSpace.NoetherianSpace.finite_irreducibleComponents
∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α], (irreducibleComponents α).Finite[Stacks Tag 0052](https://stacks.math.columbia.edu/tag/0052) ((2))
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.univproof · cited by 3,945
- Set.Finitestatement and proof · cited by 1,814
- IsClosedproof · cited by 1,639
- LE.le.antisymmproof · cited by 507
- Set.sUnionproof · cited by 392
- Set.Finite.subsetproof · cited by 285
- Set.subset_univproof · cited by 228
- IsIrreducibleproof · cited by 59
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0
- AlgebraicGeometry.finite_irreducibleComponents_of_isNoetherianproof · cited by 0