reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem Th33:
  for A being Subset of R^1 st A is closed open holds A = {} or A = REAL
proof
  let A be Subset of R^1;
  assume A is closed open;
  then reconsider A as closed open Subset of R^1;
  A = {} or A = [#]R^1 by Th32;
  hence thesis by TOPMETR:17;
end;
