Mathlib Map

Theorems · Theorem · general topology

interior_Iio

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIciTopology α] {a : α},
  interior (Set.Iio a) = Set.Iio a
Defined in
Mathlib.Topology.Order.OrderClosed
Cited by
3 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceLinearOrderClosedIciTopology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

interior_Ico · cited by 12interior_IcouniqueDiffWithinAt_Iio · cited by 4uniqueDiffWithinAt_Iiofrontier_Iio' · cited by 1frontier_Iio'Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderSet.Iio · cited by 1166Set.Iiointerior · cited by 714interiorClosedIciTopology · cited by 156ClosedIciTopologyIsOpen.interior_eq · cited by 58IsOpen.interior_eqisOpen_Iio · cited by 38isOpen_Iiointerior_IioCITED BYCITES

Cites8

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

Cited by3

Results whose statement or proof uses this declaration.