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- W2572927286 abstract "Abstract One partially ordered set, Q , is a Tukey quotient of another, P , if there is a map (a Tukey quotient ) $phi :P to Q$ carrying cofinal sets of P to cofinal sets of Q . Two partial orders which are mutual Tukey quotients of each other are said to be Tukey equivalent . Let ${cal D}_{rm{}} $ be the partially ordered set of Tukey equivalence classes of directed sets of size $ le {rm{}}$ . It is shown that ${cal D}_{rm{}} $ contains an antichain of size $2^{rm{}} $ , and so has size $2^{rm{}} $ . The elements of the antichain are of the form ${cal K}left( M right)$ , the set of compact subsets of a separable metrizable space M , ordered by inclusion. The order structure of such ${cal K}left( M right)$ ’s under Tukey quotients is investigated. Relative Tukey quotients are introduced. Applications are given to function spaces and to the complexity of weakly countably determined Banach spaces and Gul’ko compacta." @default.
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- W2572927286 date "2016-03-01" @default.
- W2572927286 modified "2023-10-17" @default.
- W2572927286 title "THE TUKEY ORDER ON COMPACT SUBSETS OF SEPARABLE METRIC SPACES" @default.
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- W2572927286 doi "https://doi.org/10.1017/jsl.2015.49" @default.
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