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

theorem Th32:
  for f being Function of TOP-REAL 2,R^1 st (for p being Point of
  TOP-REAL 2 holds f.p=proj2.p) holds f is continuous
proof
  let f be Function of TOP-REAL 2,R^1;
  assume
A1: for p being Point of TOP-REAL 2 holds f.p=proj2.p;
  reconsider f as Function of the TopStruct of TOP-REAL 2, R^1;
  (TOP-REAL 2)|([#](TOP-REAL 2))=the TopStruct of TOP-REAL 2 by TSEP_1:93;
  then f is continuous by A1,JGRAPH_2:30;
  hence thesis by PRE_TOPC:32;
end;
