Theorems · Theorem · general topology

Dense.exists_ge

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

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderClosedIicTopologyNoMaxOrder