Require Export TopologicalSpaces.
Section Subspace.
Variable X:TopologicalSpace.
Variable A:Ensemble (point_set X).
Definition SubspaceTopology : TopologicalSpace :=
WeakTopology1 (proj1_sig (P:=fun x:point_set X => In A x)).
Definition subspace_inc : point_set SubspaceTopology ->
point_set X :=
proj1_sig (P:=fun x:point_set X => In A x).

Lemma subspace_inc_continuous:
continuous subspace_inc.