Theorems · Theorem · general topology

closure_Iio

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α] (a : α)
  [NoMinOrder α], closure (Set.Iio a) = Set.Iic a

The closure of the interval (-∞, a) is the interval (-∞, a].

Defined in

Mathlib.Topology.Order.DenselyOrdered

Cited by

5 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyDenselyOrderedNoMinOrder