reserve FT for non empty RelStr,
  A,B,C for Subset of FT;

theorem
  for A being Subset of FT st FT is filled symmetric & A
  is_a_component_of FT holds A is closed
proof
  let A be Subset of FT;
  assume that
A1: FT is filled symmetric and
A2: A is_a_component_of FT;
  A is connected by A2;
  then
A3: A^b is connected by A1,Th35;
  A c= A^b by A1,FIN_TOPO:13;
  hence A = A^b by A2,A3;
end;
