Theorems · Theorem · real analysis

ContinuousWithinAt.leftLim_eq

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace β] [inst_2 : TopologicalSpace α]
  [OrderTopology α] [T2Space β] {f : α → β} {a : α}, ContinuousWithinAt f (Set.Iic a) a → Function.leftLim f a = f a

Defined in

Mathlib.Topology.Order.LeftRightLim

Cited by

4 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceTopologicalSpaceOrderTopologyT2Space