reserve X for TopSpace;

theorem Th1:
  for X being TopStruct, X0 being SubSpace of X holds the carrier
  of X0 is Subset of X
proof
  let X be TopStruct, X0 be SubSpace of X;
  reconsider A = [#]X0 as Subset of [#]X by PRE_TOPC:def 4;
  A c= [#]X;
  hence thesis;
end;
