  Theorem: The topological partition relation omega^{*}-> (Y)^{1}_{2}
  (a) fails for every space Y with |Y| >= 2^c ;
  (b) holds for Y discrete if and only if |Y| <= c;
  (c) holds for certain non-discrete P-spaces Y ;
  (d) fails for Y= omega cup {p} with p in omega^{*} ;
  (e) fails for Y infinite and countably compact.
