Theorems · Theorem · general topology
closure_singleton_eq_Iic
∀ {X : Type u_1} [inst : TopologicalSpace X] (x : X), closure {x} = Set.Iic x- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.extproof · cited by 2,266
- closurestatement · cited by 1,254
- Set.Iicstatement · cited by 1,111
- specializes_iff_mem_closureproof · cited by 11
- specializationPreorderstatement · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- specializingMap_iff_stableUnderSpecialization_image_singletonproof · cited by 2
- Union_closure_singleton_eq_iffproof · cited by 1
- specializingMap_iff_closure_singletonproof · cited by 1