Theorems · Theorem · general topology

Filter.Tendsto.prodMap_nhds

∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {x : X} {y : Y} {z : Z} {w : W} {f : X → Y} {g : Z → W},
  Filter.Tendsto f (nhds x) (nhds y) →
    Filter.Tendsto g (nhds z) (nhds w) → Filter.Tendsto (Prod.map f g) (nhds (x, z)) (nhds (y, w))

Defined in

Mathlib.Topology.Constructions.SumProd

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace