reserve X1, X2, Y for non empty RelStr,
  f for Function of [:X1, X2:], Y,
  x for Element of X1,
  y for Element of X2;

theorem Th21:
  for S being non empty TopSpace, T being non empty reflexive
TopSpace-like TopRelStr, x being set holds x is continuous Function of S, T iff
  x is Element of ContMaps (S, T)
proof
  let S be non empty TopSpace, T be non empty reflexive TopSpace-like
  TopRelStr, x be set;
  thus x is continuous Function of S, T implies x is Element of ContMaps (S, T
  ) by Def3;
  assume x is Element of ContMaps (S, T);
  then ex f being Function of S, T st x = f & f is continuous by Def3;
  hence thesis;
end;
