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Theorems · Theorem · general topology

isPreconnected_uIoo

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : ConditionallyCompleteLinearOrder α] [OrderTopology α]
  [DenselyOrdered α] {a b : α}, IsPreconnected (Set.uIoo a b)
Defined in
Mathlib.Topology.Order.IntermediateValue
Cited by
1 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceConditionallyCompleteLinearOrderOrderTopologyDenselyOrdered
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Around this declaration

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

isConnected_uIoo · cited by 1isConnected_uIooTopologicalSpace · cited by 24529TopologicalSpaceOrderTopology · cited by 1355OrderTopologyConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…DenselyOrdered · cited by 471DenselyOrderedIsPreconnected · cited by 205IsPreconnectedSet.uIoo · cited by 68Set.uIooisPreconnected_Ioo · cited by 6isPreconnected_IooisPreconnected_uIooCITED BYCITES

Cites7

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Cited by1

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