proposition: Lemma continuous_tpair {U V : TopologicalSpace} : continuous2d (W := TopologyDirprod U V) (λ (x : U) (y : V), (x,,y)).
proof: Proof. intros x y P. apply hinhuniv. intros O. simple refine (filter_imply _ _ _ _ _). - exact (pr1 O). - exact (pr2 (pr2 O)). - generalize (pr2 (pr1 O) _ (pr1 (pr2 O))). apply hinhfun. intros Ho. exists (pr1 Ho), (pr1 (pr2 Ho)). repeat split. + apply (pr2 (neighborhood_isOpen _)). * exact (pr2 (pr1 (pr2 (pr2 Ho)))). * exact (pr1 (pr1 (pr2 (pr2 Ho)))). + apply (pr2 (neighborhood_isOpen _)). * exact (pr2 (pr1 (pr2 (pr2 (pr2 Ho))))). * exact (pr1 (pr1 (pr2 (pr2 (pr2 Ho))))). + exact (pr2 (pr2 (pr2 (pr2 Ho)))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Topology.Filters UniMath.Algebra.Groups UniMath.Algebra.DivisionRig UniMath.Algebra.ConstructiveStructures