
theorem Th55:
  for T being non empty TopSpace, S being non empty SubSpace of T
  st S is_a_retract_of T holds S is_Retract_of T
proof
  let T be non empty TopSpace, S be non empty SubSpace of T;
  reconsider g = incl(S,T) as continuous Function of S,T by Th53;
  given f be continuous Function of T,S such that
A1: f is being_a_retraction;
  take g,f;
  thus thesis by A1,Th54;
end;
