proposition: Corollary quotient_continuous: forall (X:TopologicalSpace) (f g:point_set X -> point_set RTop) (x0:point_set X), continuous_at f x0 -> continuous_at g x0 -> g x0 <> 0 -> continuous_at (fun x:point_set X => f x / g x) x0 (Y:=RTop).
proof: Proof. intros. apply continuous_composition_at_2arg; trivial. apply Rdiv_continuous; trivial. Qed.
imports: RTopology ProductTopology Homeomorphisms ContinuousFactorization Coq(FunctionalExtensionality Lra ProofIrrelevance) ZornsLemma(EnsembleProduct EnsemblesTactics)