Require Export SeparatednessAxioms.
Require Export SubspaceTopology.

(* Specifications: *)
Lemma compact_closed: forall (X:TopologicalSpace)
(S:Ensemble (point_set X)), Hausdorff X ->
compact (SubspaceTopology S) -> closed S.
Lemma closed_compact: forall (X:TopologicalSpace) (S:Ensemble (point_set X)),
compact X -> closed S -> compact (SubspaceTopology S).
Lemma compact_image: forall {X Y:TopologicalSpace}
(f:point_set X->point_set Y),
compact X -> continuous f -> surjective f -> compact Y.
Lemma compact_Hausdorff_impl_normal_sep: forall X:TopologicalSpace,
compact X -> Hausdorff X -> normal_sep X.