# 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.

- published version (10p)

Bib entry

@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}, doi = {10.1111/j.1749-6632.1993.tb52510.x}, mrclass = {54B05 (04A20 54A20 54D40 54G10)}, mrnumber = {1277844}, mrreviewer = {J. E. Vaughan}, doi = {10.1111/j.1749-6632.1993.tb52510.x}, publisher = {New York Acad. Sci., New York}, note = {\href{https://arxiv.org/abs/math/9305206}{arXiv: math/9305206}}, arxiv_number = {math/9305206} }