Theorems · Theorem · general topology

eq_lim_at_left_extendFrom_uIoo

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [DenselyOrdered α]
  [OrderTopology α] [inst_4 : TopologicalSpace β] {f : α → β} {a b : α} {la : β} [T2Space β],
  a ≠ b → Filter.Tendsto f (nhdsWithin a (Set.uIoo a b)) (nhds la) → extendFrom (Set.uIoo a b) f a = la

Defined in

Mathlib.Topology.Order.ExtendFrom

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderDenselyOrderedOrderTopologyTopologicalSpaceT2Space