Theorems · Theorem · general topology

dense_of_exists_between

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [Nontrivial α] {s : Set α},
  (∀ ⦃a b : α⦄, a < b → ∃ c ∈ s, c ∈ Set.Ioo a b) → Dense s

Defined in

Mathlib.Topology.Order.Basic

Cited by

6 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyNontrivial