English
The restricted action of a Subalgebra on a topological space inherits continuity from the ambient action; i.e., if A acts continuously on X, then any subalgebra S ⊆ A also acts continuously on X.
Русский
Ограниченное действие подалгебры на топологическом пространстве наследует непрерывность от внешнего действия: если A действует непрерывно на X, то и подалгебра S ⊆ A действует непрерывно на X.
LaTeX
$$$\\operatorname{ContinuousSMul}~S~X$$$
Lean4
/-- The inclusion of the base ring in a topological algebra as a continuous linear map. -/
@[simps]
def algebraMapCLM : R →L[R] A :=
{ Algebra.linearMap R A with
toFun := algebraMap R A
cont := continuous_algebraMap R A }
