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 Th73:
  P is bounded implies for g being continuous RealMap of TOP-REAL
  2 holds Cl(g.:P) c= g.:Cl P
proof
  assume P is bounded;
  then
A1: Cl P is compact by Th72;
  let g be continuous RealMap of TOP-REAL 2;
  reconsider f = g as Function of TOP-REAL 2, R^1 by TOPMETR:17;
  f is continuous by JORDAN5A:27;
  then f.:Cl P is closed by A1,COMPTS_1:7,WEIERSTR:9;
  then
A2: g.:Cl P is closed by JORDAN5A:23;
  g.:P c= g.:Cl P by PRE_TOPC:18,RELAT_1:123;
  hence thesis by A2,MEASURE6:57;
end;
