Theorems · Theorem · general topology

Dense.exists_lt

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] [NoMinOrder α] {s : Set α},
  Dense s → ∀ (x : α), ∃ y ∈ s, y < x

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderClosedIciTopologyNoMinOrder