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Theorems · Theorem · general topology

IsPreconnected.ordConnected

∀ {α : Type v} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderClosedTopology α] {s : Set α},
  IsPreconnected s → s.OrdConnected
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
LinearOrderTopologicalSpaceOrderClosedTopology
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isPreconnected_iff_ordConnected · cited by 1isPreconnected_iff_ordCon…IsPreconnected.measurableSet · cited by 0IsPreconnected.measurable…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderOrderClosedTopology · cited by 445OrderClosedTopologyIsPreconnected · cited by 205IsPreconnectedSet.OrdConnected · cited by 161Set.OrdConnectedIsPreconnected.Icc_subset · cited by 4IsPreconnected.Icc_subsetIsPreconnected.ordConnectedCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.