Require Export CountabilityAxioms.

(* Specifications: *)
Lemma metrizable_impl_first_countable: forall X:TopologicalSpace,
metrizable X -> first_countable X.
Lemma metrizable_separable_impl_second_countable:
forall X:TopologicalSpace, metrizable X -> separable X ->
second_countable X.
Lemma metrizable_Lindelof_impl_second_countable:
forall X:TopologicalSpace, metrizable X -> Lindelof X ->
second_countable X.