Theorems · Theorem · general topology
isClosed_Iic
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIicTopology α] {a : α}, IsClosed (Set.Iic a)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- IsClosedstatement · cited by 1,639
- Set.Iicstatement · cited by 1,111
- ClosedIicTopologystatement and proof · cited by 115
- ClosedIicTopology.isClosed_Iicproof · cited by 1
Cited by23
Results whose statement or proof uses this declaration.
- le_of_tendstoproof · cited by 32
- measurableSet_Iicproof · cited by 23
- isClosed_Iccproof · cited by 17
- IsCompact.exists_isLeastproof · cited by 9
- Metric.isClosed_cthickeningproof · cited by 5
- closure_Iicproof · cited by 4
- geometric_hahn_banach_of_nonempty_interiorproof · cited by 3
- WeakDual.isClosed_polarproof · cited by 3
- ContinuousLinearMap.is_weak_closed_closedBallproof · cited by 3
- upperBounds_closureproof · cited by 2
- Dense.upperBounds_imageproof · cited by 2
- IsLowerSet.isClosedproof · cited by 1