Baumgartner, James E. Partition relations for countable topological spaces. (English) Zbl 0647.05005 J. Comb. Theory, Ser. A 43, 178-195 (1986). We consider partition relations for pairs of elements of a countable topological space. For spaces with infinitely many nonempty derivatives a strong negative theorem is obtained. For example, it is possible to partition the pairs of rationals into countably many pieces so that every homeomorph of the rationals contains a pair from every piece. Some positive results are also proved for ordinal spaces of the form \(\omega^{\alpha}+1\), where \(\alpha\) is countable. Cited in 1 ReviewCited in 16 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 03E05 Other combinatorial set theory Keywords:partition relations; countable topological space PDFBibTeX XMLCite \textit{J. E. Baumgartner}, J. Comb. Theory, Ser. A 43, 178--195 (1986; Zbl 0647.05005) Full Text: DOI References: [1] Devlin, D., Some Partition Theorems and Ultrafilters on ω, (Ph.D. dissertation (1979), Dartmouth College) [2] Erdös, P.; Hajnal, A., Unsolved and solved problems in set theory, (Proc. Sympos. Pure Math., Vol. 25 (1974), Amer. Math. Soc: Amer. Math. Soc Providence, R. I), 267-287 [3] Jech, T., Set Theory (1978), Academic Press: Academic Press New York · Zbl 0419.03028 [4] Kunen, K., Set Theory (1980), North-Holland: North-Holland Amsterdam This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.