Theorems · Theorem · general topology
closure_sUnion_irreducibleComponents_sdiff_singleton
∀ {X : Type u_1} [inst : TopologicalSpace X],
(irreducibleComponents X).Finite → ∀ Z ∈ irreducibleComponents X, closure (⋃₀ (irreducibleComponents X \ {Z}))ᶜ = Z- Defined in
- Mathlib.Topology.Irreducible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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.univproof · cited by 3,945
- Compl.complstatement and proof · cited by 2,925
- IsOpenproof · cited by 2,400
- Set.Finitestatement and proof · cited by 1,814
- closurestatement and proof · cited by 1,254
- Set.sUnionstatement and proof · cited by 392
- Set.Subset.antisymmproof · cited by 213
- Set.singleton_subset_iffproof · cited by 206
- Set.mem_singletonproof · cited by 183
- Set.sdiff_subsetproof · cited by 156
Cited by2
Results whose statement or proof uses this declaration.