English
If A is a topological module over a commutative semiring R with a compatible star structure, then starL is a continuous semilinear equivalence A ≃L⋆[R] A.
Русский
Если A — топологический модуль над коммутативным полугруппой R с совместимым звездовым действием, то starL — непрерывное полумодулярное эквивалентное отображение A ≃L⋆[R] A.
LaTeX
$$$\text{starL}(R,A): A \simeq_{L⋆[R]} A$$$
Lean4
/-- If `A` is a topological module over a commutative `R` with compatible actions,
then `star` is a continuous semilinear equivalence. -/
@[simps!]
def starL (R : Type*) {A : Type*} [CommSemiring R] [StarRing R] [AddCommMonoid A] [StarAddMonoid A] [Module R A]
[StarModule R A] [TopologicalSpace A] [ContinuousStar A] : A ≃L⋆[R] A
where
toLinearEquiv := starLinearEquiv R
continuous_toFun := continuous_star
continuous_invFun := continuous_star
