Theorems · Theorem · general topology
Union_closure_singleton_eq_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, ⋃ x ∈ s, closure {x} = s ↔ StableUnderSpecialization s- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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.
Cites10
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.iUnionstatement and proof · cited by 2,483
- closurestatement and proof · cited by 1,254
- Set.Iicproof · cited by 1,111
- Set.iUnion_congr_Propproof · cited by 374
- IsLowerSetproof · cited by 167
- StableUnderSpecializationstatement · cited by 32
- closure_singleton_eq_Iicproof · cited by 3
- coe_lowerClosureproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- stableUnderSpecialization_iff_Union_eqproof · cited by 1