Tukey Order, Calibres and the Rationals

2016/06/21 by Gartside, Paul, Mamatelashvili, Ana · 2 citations
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1606.06493

Abstract

One partially ordered set, Q, is a Tukey quotient of another, P, denoted P ≥_T Q, if there is a map ϕ: P → Q carrying cofinal sets of P to cofinal sets of Q. Let X be a space and denote by K(X) the set of compact subsets of X, ordered by inclusion. For certain separable metrizable spaces M, Tukey upper and lower bounds of K(M) are calculated. Results on invariants of K(M)'s are deduced. The structure of all K(M)'s under ≤_T is investigated. Particular emphasis is placed on the position of K(M) when M is: completely metrizable, the rationals ℚ, co-analytic or analytic.

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