reserve a for Real;
reserve p,q for Point of TOP-REAL 2;

theorem Th6:
  for X being non empty TopSpace, f1 being Function of X,R^1 st f1
is continuous holds ex g being Function of X,R^1 st (for p being Point of X,r1
  being Real st f1.p=r1 holds g.p=r1^2) & g is continuous
proof
  let X be non empty TopSpace, f1 be Function of X,R^1;
  assume f1 is continuous;
  then consider g1 being Function of X,R^1 such that
A1: for p being Point of X,r1 being Real st f1.p=r1 holds g1.p=r1
  *r1 and
A2: g1 is continuous by JGRAPH_2:22;
  for p being Point of X,r1 being Real st f1.p=r1 holds g1.p=r1^2 by A1;
  hence thesis by A2;
end;
