English
The canonical forgetful map from the space of continuous multilinear maps to the space of multilinear maps is injective.
Русский
Каноническое отображение, переходящее от непрерывных многолинейных отображений к обычным многообразным отображениям, вводит инъекцию.
LaTeX
$$$\\mathrm{toMultilinearMap}: \\text{ContinuousMultilinearMap} \\to \\text{MultilinearMap}$ is injective; if f.toMultilinearMap = g.toMultilinearMap, then f = g.$$
Lean4
/-- If `R` is a topological ring and `D` is an `R`-algebra, finite as an `R`-module,
and if `D` is given the module topology, then `D` is a topological ring. -/
theorem isTopologicalRing : IsTopologicalRing D where
-- Proof: we have already checked all the axioms above.
continuous_add := (toContinuousAdd R D).1
continuous_mul := continuous_mul_of_finite R D
continuous_neg := continuous_neg R D
