reserve T for TopStruct;
reserve GX for TopSpace;

theorem
  for A being Subset of T st A <> {}T ex x being Point of T st x in A
proof
  let A be Subset of T;
  set x = the Element of A;
  assume
A1: A <> {}T;
  then x is Point of T by TARSKI:def 3;
  hence thesis by A1;
end;
