Theorems · Theorem · general topology

continuousWithinAt_Ioc_iff_Iic

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [ClosedIicTopology α]
  [inst_3 : TopologicalSpace β] {a b : α} {f : α → β},
  a < b → (ContinuousWithinAt f (Set.Ioc a b) b ↔ ContinuousWithinAt f (Set.Iic b) b)

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderClosedIicTopologyTopologicalSpace