reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;

theorem Th82:
  for A,B being Subset of TOP-REAL n holds A is bounded or B is
  bounded implies A /\ B is bounded
proof
  let A,B be Subset of TOP-REAL n;
  assume
A1: A is bounded or B is bounded;
  per cases by A1;
  suppose
    A is bounded;
    hence thesis by RLTOPSP1:42,XBOOLE_1:17;
  end;
  suppose
    B is bounded;
    hence thesis by RLTOPSP1:42,XBOOLE_1:17;
  end;
end;
