Continuous cofinal maps on ultrafilters
Continuous cofinal maps on ultrafilters
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发表时间：
2011
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通讯作者：
Natasha Dobrinen
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作者：
Natasha Dobrinen
An ultrafilter $mathcal{U}$ on a countable base {em has continuous Tukey reductions} if whenever an ultrafilter $mathcal{V}$ is Tukey reducible to $mathcal{U}$, then every monotone cofinal map $f:mathcal{U}
amathcal{V}$ is continuous when restricted to some cofinal subset of $mathcal{U}$.
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 $mathcal{U}$ is Tukey reducible to a p-point then $mathcal{U}$ 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 $vec{mathcal{U}}$-trees.
An ultrafilter $mathcal{U}$ on a countable base {em has continuous Tukey reductions} if whenever an ultrafilter $mathcal{V}$ is Tukey reducible to $mathcal{U}$, then every monotone cofinal map $f:mathcal{U}
amathcal{V}$ is continuous when restricted to some cofinal subset of $mathcal{U}$.
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 $mathcal{U}$ is Tukey reducible to a p-point then $mathcal{U}$ 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 $vec{mathcal{U}}$-trees.