Theorems · Theorem · general topology
closure_uIoo
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α},
a ≠ b → closure (Set.uIoo a b) = Set.uIcc a b- Defined in
- Mathlib.Topology.Order.DenselyOrdered
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccproof · cited by 1,702
- OrderTopologystatement and proof · cited by 1,355
- closurestatement · cited by 1,254
- DenselyOrderedstatement and proof · cited by 471
- Set.uIccstatement · cited by 393
- Set.uIoostatement · cited by 68
- closure_Iooproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- eq_lim_at_left_extendFrom_uIooproof · cited by 1
- eq_lim_at_right_extendFrom_uIooproof · cited by 1