reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem Th37:
  for X being non empty set, x0 being Element of X for A being non
  empty Subset of x0-PointClTop(X) holds Cl A = A \/ {x0}
proof
  let X be non empty set;
  let x0 be Element of X;
  let A be non empty Subset of x0-PointClTop(X);
  thus Cl A = IFEQ(A,{},A,A \/ {x0}/\X) by Def7
    .= A \/ {x0}/\X by FUNCOP_1:def 8
    .= A \/ {x0} by XBOOLE_1:28;
end;
