Galois-Tukey connection involving sets of metrics

Abstract

Kada proved in a previous paper (Topology Appl., 2009) that the collection of compatible metrics on a locally compact separable metrizable space has the same cofinal type, in the sense of Tukey relation, as the set of functions from ω to ω with respect to eventually dominating order. By generalizing this result, we characterize the order structure of the collection of compatible metrics on a separable metrizable space in terms of generalized Galois-Tukey connection.