2011/10/19 by Natasha Dobrinen, Dobrinen, Natasha
Computer Science · Mathematics · #03E #54D #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Limits and Structures in Graph Theory #Logic (math.LO) #math.GN #math.LO #msc:03E #msc:54D
paper · pdf · doi:10.48550/arxiv.1110.4154
25 pages, submitted
arxiv created 2011/10/19 · openalex publication_date 2011/10/19 · arxiv updated 2011/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An ultrafilter U on a countable base \em has continuous Tukey reductions if whenever an ultrafilter V is Tukey reducible to U, then every monotone cofinal map f:U\raV is continuous when restricted to some cofinal subset of U. In the first part of the paper, we give mild conditions under which the property of having continuous Tukey reductions is inherited under Tukey reducibility. In particular, if U is Tukey reducible to a p-point then U has continuous Tukey reductions. In the second part, we show that any countable iteration of Fubini products of p-points has Tukey reductions which are continuous with respect to its topological Ramsey space of U-trees.