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.