English
From an unbundled topological module M one constructs an object in TopModuleCat(R).
Русский
Из неупакованного топологического модуля M строится объект в TopModuleCat(R).
LaTeX
$$$\text{of}_R: M \mapsto \mathrm{TopModuleCat}(R)$-объект$$
Lean4
/-- Make an object in `TopModuleCat R` from an unbundled topological module. -/
abbrev of (M : Type v) [AddCommGroup M] [Module R M] [TopologicalSpace M] [ContinuousAdd M] [ContinuousSMul R M] :
TopModuleCat R :=
have : ContinuousNeg M := ⟨by convert continuous_const_smul (-1 : R) (T := M); ext; simp⟩
have : IsTopologicalAddGroup M := ⟨⟩
⟨.of R M⟩