Theorems · Theorem · general topology
closure_Ici
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Preorder α] [ClosedIciTopology α] (a : α),
closure (Set.Ici a) = Set.Ici a- Defined in
- Mathlib.Topology.Order.OrderClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- closurestatement · cited by 1,254
- Set.Icistatement · cited by 1,070
- ClosedIciTopologystatement and proof · cited by 156
- IsClosed.closure_eqproof · cited by 139
- isClosed_Iciproof · cited by 40
Cited by4
Results whose statement or proof uses this declaration.
- closure_halfSpaceproof · cited by 1
- frontier_Ici'proof · cited by 1
- Complex.frontier_setOfPred_le_re_and_im_leproof · cited by 1
- Complex.frontier_setOfPred_le_re_and_le_improof · cited by 1