Theorems · Theorem · general topology

Dense.exists_between

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] [DenselyOrdered α]
  {s : Set α}, Dense s → ∀ {x y : α}, x < y → ∃ z ∈ s, z ∈ Set.Ioo x y

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

5 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderClosedTopologyDenselyOrdered