Theorems · Theorem · functional analysis

IsModuleTopology.continuous_mul_of_finite

∀ (R : Type u_1) [inst : CommRing R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R] (D : Type u_2)
  [inst_3 : Ring D] [inst_4 : Algebra R D] [Module.Finite R D] [inst_6 : TopologicalSpace D] [IsModuleTopology R D],
  Continuous fun ab => ab.1 * ab.2

If D is an R-algebra, finite as an R-module, and if D has the module topology, then multiplication on D is automatically continuous.

Defined in

Mathlib.Topology.Algebra.Module.ModuleTopology

Cited by

0 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingTopologicalSpaceIsTopologicalRingRingAlgebraModule.FiniteTopologicalSpaceIsModuleTopology