Theorems · Theorem · general topology

IsOpen.exists_Ioo_subset

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [Nontrivial α] {s : Set α},
  IsOpen s → s.Nonempty → ∃ a b, a < b ∧ Set.Ioo a b ⊆ s

Defined in

Mathlib.Topology.Order.Basic

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyNontrivial