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

theorem Th15:
  for p being Point of Euclid 2,r being Real, B being Subset of
  TOP-REAL 2 st B=cl_Ball(p,r) holds B is compact
proof
  let p be Point of Euclid 2,r be Real, B be Subset of TOP-REAL 2;
  assume B=cl_Ball(p,r);
  then B is bounded closed by Th14;
  hence thesis by TOPREAL6:79;
end;
