Theorems · Theorem · general topology

Filter.tendsto_nhds_min_right

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] {f : β → α}
  {l : Filter β} {a : α},
  Filter.Tendsto f l (nhdsWithin a (Set.Iio a)) → Filter.Tendsto (fun i => min a (f i)) l (nhdsWithin a (Set.Iio a))

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderClosedTopology