Theorems · Theorem · general topology

Set.OrdConnected.isPreconnected

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
  [DenselyOrdered α] {s : Set α}, s.OrdConnected → IsPreconnected s

Defined in

Mathlib.Topology.Order.IntermediateValue

Cited by

9 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceConditionallyCompleteLinearOrderOrderTopologyDenselyOrdered