Topological Partition Relations to the Form $\omega^*\rightarrow(Y)^1_2$

by Comfort and Kato and Shelah. [CKSh:440]
Proc Seventh Summer Conference at the University of Wisconsin, Papers on General Topology and Applications, 1993
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.


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