Theorems · Theorem · functional analysis

ContinuousLinearMap.cont

∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {M : Type u_3}
  [inst_2 : TopologicalSpace M] [inst_3 : AddCommMonoid M] {M₂ : Type u_4} [inst_4 : TopologicalSpace M₂]
  [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M] [inst_7 : Module S M₂] (self : M →SL[σ] M₂),
  Continuous (↑self).toFun

Continuous linear maps between modules. We only put the type classes that are necessary for the definition, although in applications M and M₂ will be topological modules over the topological ring R.

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

17 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

SemiringSemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule