reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;

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;
