reserve e,u for set;

theorem Th1:
  for X being TopStruct, Y being SubSpace of X holds the carrier
  of Y c= the carrier of X
proof
  let X be TopStruct, Y be SubSpace of X;
  the carrier of Y = [#]Y & the carrier of X = [#]X;
  hence thesis by PRE_TOPC:def 4;
end;
