theorem Th17:
  for S, T being TopSpace st S, T are_homeomorphic & S is
  connected holds T is connected
proof
  let S, T be TopSpace;
  given f being Function of S,T such that
A1: f is being_homeomorphism;
A2: rng f = [#]T by A1;
  assume
A3: S is connected;
  dom f = [#]S by A1;
  then f.:[#]S = [#]T by A2,RELAT_1:113;
  hence thesis by A1,A3,CONNSP_1:14;
end;
