### 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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