proposition: Corollary const_multiple_continuous: forall (X:TopologicalSpace) (f:point_set X -> point_set RTop) (c:R) (x:point_set X), continuous_at f x -> continuous_at (fun x:point_set X => c * f x) x (Y:=RTop).
proof: Proof. intros. apply continuous_composition_at; trivial. apply continuous_func_continuous_everywhere, const_multiple_func_continuous. Qed.
imports: RTopology ProductTopology Homeomorphisms ContinuousFactorization Coq(FunctionalExtensionality Lra ProofIrrelevance) ZornsLemma(EnsembleProduct EnsemblesTactics)