Theorems · Theorem · general topology
isClosed_Ici
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIciTopology α] {a : α}, IsClosed (Set.Ici a)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 40 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.Icistatement · cited by 1,070
- ClosedIciTopologystatement and proof · cited by 156
- ClosedIciTopology.isClosed_Iciproof · cited by 1
Cited by40
Results whose statement or proof uses this declaration.
- ge_of_tendstoproof · cited by 29
- measurableSet_Iciproof · cited by 26
- isClosed_Iccproof · cited by 17
- closure_Ioi'proof · cited by 5
- MeasureTheory.integral_mono_measureproof · cited by 5
- closure_Iciproof · cited by 4
- NNReal.isClosedEmbedding_coeproof · cited by 4
- Integrable.norm_condExp_rpow_leproof · cited by 3
- ConvexOn.map_condExp_rnDeriv_leproof · cited by 3
- contentRegular_rieszContentproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2
- MeasureTheory.L1.setToL1_nonnegproof · cited by 2