Theorems · Theorem · general topology

DedekindCut.continuous_principal

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
  [inst_3 : TopologicalSpace (DedekindCut α)] [OrderTopology (DedekindCut α)],
  Continuous fun a => DedekindCut.principal a

Defined in: Mathlib.Topology.Order.Completion
Cited by: 1 results in Mathlib
Foundations: Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace OrderTopology TopologicalSpace OrderTopology

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

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
LinearOrderstatement and proof · cited by 8,572
Set.preimageproof · cited by 4,946
Continuousstatement · cited by 2,592
Set.iUnionproof · cited by 2,483
IsOpenproof · cited by 2,400
Set.extproof · cited by 2,266
Set.Ioiproof · cited by 1,463
OrderTopologystatement and proof · cited by 1,355
Set.Iioproof · cited by 1,166
isOpen_Ioiproof · cited by 43

Cited by1

Results whose statement or proof uses this declaration.

Order.exists_dense_continuous_completionproof · cited by 0