Theorems · Theorem · general topology

IsPreconnected.Ioi_csInf_subset

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α] {s : Set α},
  IsPreconnected s → BddBelow s → ¬BddAbove s → Set.Ioi (sInf s) ⊆ s

Defined in

Mathlib.Topology.Order.IntermediateValue

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceConditionallyCompleteLinearOrderOrderTopology