Topological partition relations to the form omega^*-> (Y)^1_2
arXiv:math/9305206 · doi:10.1111/j.1749-6632.1993.tb52510.x
Abstract
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.