Topological Ramsey Spaces and Metrically Baire Sets
Publication Date
5-15-2015
Document Type
Article
Organizational Units
Mathematics
Keywords
Baire set, Ramsey space, Parameter word
Abstract
We characterize a class of topological Ramsey spaces such that each element R" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">R of the class induces a collection {Rk}k{Rk}kRk" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">Rk is a subspace of the corresponding space of length-k approximation sequences with the Tychonoff, equivalently metric, topology. This answers a question of S. Todorcevic and generalizes some results of Carlson, Carlson–Simpson, Prömel–Voigt, and Voigt. We also present a new family of topological Ramsey spaces contained in the aforementioned class which generalize the spaces of ascending parameter words of Carlson–Simpson and Prömel–Voigt and the spaces FINm[∞]" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">FINm[∞], 0
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Recommended Citation
Dobrinen, Natasha, and Mijares, José G. “Topological Ramsey Spaces and Metrically Baire Sets.” Journal of Combinatorial Theory. Series A, vol. 135, 2015, pp. 161–180. doi: 10.1016/j.jcta.2015.05.001.