reserve X for TopSpace;

theorem Th10:
  for X being non empty TopStruct, A0 being non empty Subset of X
  ex X0 being strict non empty SubSpace of X st A0 = the carrier of X0
proof
  let X be non empty TopStruct, A0 be non empty Subset of X;
  take X0 = X|A0;
  A0 = [#]X0 by PRE_TOPC:def 5;
  hence thesis;
end;
