theorem :: JORDAN18:2, AK, 21.02.2006
  for S,T being non empty TopSpace, f being Function of S,T, A being
Subset of T st f is being_homeomorphism & A is connected holds f"A is connected
proof
  let S,T be non empty TopSpace, f be Function of S,T, A be Subset of T such
  that
A1: f is being_homeomorphism and
A2: A is connected;
  f" is continuous by A1;
  then
A3: f".:A is connected by A2,Th61;
  rng f = [#]T & f is one-to-one by A1;
  hence thesis by A3,Th55;
end;
