Theorems · Theorem · general topology

isClosed_Ioo_iff

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α},
  IsClosed (Set.Ioo a b) ↔ b ≤ a

Set.Ioo a b is only closed if it is empty.

Defined in

Mathlib.Topology.Order.DenselyOrdered

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyDenselyOrdered