Theorems · Theorem · functional analysis

ContinuousLinearEquiv.continuous_toFun

∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {σ' : S →+* R}
  [inst_2 : RingHomInvPair σ σ'] [inst_3 : RingHomInvPair σ' σ] {M : Type u_3} [inst_4 : TopologicalSpace M]
  [inst_5 : AddCommMonoid M] {M₂ : Type u_4} [inst_6 : TopologicalSpace M₂] [inst_7 : AddCommMonoid M₂]
  [inst_8 : Module R M] [inst_9 : Module S M₂] (self : M ≃SL[σ] M₂), Continuous (↑↑self).toFun

Continuous linear equivalences 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 semiring R.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule