Theorems · Theorem · general topology

DenselyOrdered.subsingleton_of_discreteTopology

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [DenselyOrdered α]
  [DiscreteTopology α], Subsingleton α

If the order topology for a dense linear ordering is discrete, the space has at most one point. We would prefer for this to be an instance but even at (priority := 100) this was problematic so we have deferred this issue. TODO Promote this to an instance!

Defined in

Mathlib.Topology.Order.DenselyOrdered

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceLinearOrderOrderTopologyDenselyOrderedDiscreteTopology