Theorems · Theorem · functional analysis

IsModuleTopology.continuous_of_ringHom

∀ {R : Type u_6} {A : Type u_7} {B : Type u_8} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : Semiring B] [inst_4 : TopologicalSpace R] [inst_5 : TopologicalSpace A] [IsModuleTopology R A]
  [inst_7 : TopologicalSpace B] [IsTopologicalSemiring B] (φ : A →+* B),
  Continuous ⇑(φ.comp (algebraMap R A)) → Continuous ⇑φ

Defined in

Mathlib.Topology.Algebra.Module.ModuleTopology

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringTopologicalSpaceTopologicalSpaceIsModuleTopologyTopologicalSpaceIsTopologicalSemiring