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Theorems · Theorem · general topology

interior_Ioo

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] {a b : α},
  interior (Set.Ioo a b) = Set.Ioo a b
Defined in
Mathlib.Topology.Order.OrderClosed
Cited by
3 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceLinearOrderOrderClosedTopology
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Around this declaration

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

Convex.Ioo_subset_of_mem_closure · cited by 3Convex.Ioo_subset_of_mem_…Ioo_subset_closure_interior · cited by 1Ioo_subset_closure_interi…frontier_Ioo · cited by 1frontier_IooSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderSet.Ioo · cited by 1214Set.Ioointerior · cited by 714interiorOrderClosedTopology · cited by 445OrderClosedTopologyIsOpen.interior_eq · cited by 58IsOpen.interior_eqisOpen_Ioo · cited by 54isOpen_Ioointerior_IooCITED 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.