Theorems · Theorem · general topology

Filter.Tendsto.max

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderClosedTopology α] {f g : β → α}
  {b : Filter β} {a₁ a₂ : α},
  Filter.Tendsto f b (nhds a₁) →
    Filter.Tendsto g b (nhds a₂) → Filter.Tendsto (fun b => max (f b) (g b)) b (nhds (max a₁ a₂))

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderClosedTopology