Theorems · Theorem · general topology
isClosed_Icc
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [t : OrderClosedTopology α] {a b : α},
IsClosed (Set.Icc a b)- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.Iccstatement · cited by 1,702
- IsClosedstatement · cited by 1,639
- OrderClosedTopologystatement and proof · cited by 445
- IsClosed.interproof · cited by 61
- isClosed_Iciproof · cited by 40
- isClosed_Iicproof · cited by 23
Cited by17
Results whose statement or proof uses this declaration.
- measurableSet_Iccproof · cited by 32
- closure_Iooproof · cited by 20
- closure_Iocproof · cited by 5
- closure_Iccproof · cited by 4
- closure_Icoproof · cited by 4
- image_le_of_liminf_slope_right_lt_deriv_boundary'proof · cited by 4
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_leproof · cited by 2
- setOfPred_riemannianEDist_lt_subset_nhdsproof · cited by 2
- IsClosed.Icc_subset_of_forall_exists_gtproof · cited by 2
- IsLocalHomeomorph.exists_lift_nhdsproof · cited by 1
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Icoproof · cited by 1
- closure_interior_Iccproof · cited by 1