Require Export Continuity.

Lemma func_preserving_filter_limits_is_continuous:
forall (X Y:TopologicalSpace) (f:point_set X -> point_set Y)
(x:point_set X),
(forall F:Filter (point_set X), filter_limit F x ->
filter_limit (filter_direct_image f F) (f x)) ->
continuous_at f x.