Theorems · Theorem · general topology
TopologicalSpace.vietoris.closure_finite_subsets
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : Set α), closure {t | t.Finite ∧ t ⊆ s} = 𝒫 closure s- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 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.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Set.rangeproof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Finiteproof · cited by 3,029
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- Set.Finitestatement and proof · cited by 1,814
- closurestatement and proof · cited by 1,254
- Subtype.propproof · cited by 505
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.closure_finite_subsetsproof · cited by 3