Theorems · Theorem · general topology

ContinuousMap.prodMul_apply

∀ {X : Type u_5} {Y : Type u_6} {R : Type u_7} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : CommRing R] [inst_3 : TopologicalSpace R] [inst_4 : IsTopologicalRing R] (f : C(X, R)) (g : C(Y, R))
  (p : X × Y), ((ContinuousMap.prodMul f) g) p = f p.1 * g p.2

Defined in

Mathlib.Topology.UniformSpace.ProdApproximation

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceCommRingTopologicalSpaceIsTopologicalRing