Sh:440

• Comfort, W. W., Kato, A., & Shelah, S. (1993). Topological partition relations of the form $\omega^\ast\to(Y)^1_2$. In Papers on general topology and applications (Madison, WI, 1991), Vol. 704, New York Acad. Sci., New York, pp. 70–79. arXiv: math/9305206 DOI: 10.1111/j.1749-6632.1993.tb52510.x MR: 1277844
• Abstract:
  Theorem: The topological partition relation $\omega^{*}\rightarrow(Y)^{1}_{2}$

  (a) fails for every space $Y$ with $|Y|\geq 2^{\rm \bf c}$;

  (b) holds for $Y$ discrete if and only if $|Y|\leq$ 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.

• Version 1993-08-29_10 (15p) published version (10p)

@incollection{Sh:440,
 author = {Comfort, William Wistar and Kato, Akio and Shelah, Saharon},
 title = {{Topological partition relations of the form $\omega^\ast\to(Y)^1_2$}},
 booktitle = {{Papers on general topology and applications (Madison, WI, 1991)}},
 series = {Ann. New York Acad. Sci.},
 volume = {704},
 year = {1993},
 pages = {70--79},
 publisher = {New York Acad. Sci., New York},
 mrnumber = {1277844},
 mrclass = {54B05 (04A20 54A20 54D40 54G10)},
 doi = {10.1111/j.1749-6632.1993.tb52510.x},
 note = {\href{https://arxiv.org/abs/math/9305206}{arXiv: math/9305206}},
 arxiv_number = {math/9305206}
}