Theorems · Theorem · general topology
IsClosed.upperClosure
∀ {α : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
{s : Set α}, IsClosed s → IsClosed ↑(upperClosure s)- Defined in
- Mathlib.Topology.Order.IsLUB
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- SetLike.coestatement and proof · cited by 8,199
- Set.Nonemptyproof · cited by 2,627
- IsClosedstatement and proof · cited by 1,639
- OrderTopologystatement and proof · cited by 1,355
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- BddBelowproof · cited by 401
- Set.eq_empty_or_nonemptyproof · cited by 248
- UpperSetstatement · cited by 245
- upperClosurestatement · cited by 84
- isClosed_univproof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.lowerClosureproof · cited by 0