Tsukuba Journal of Mathematics

Galois-Tukey connection involving sets of metrics

Masaru Kada and Yasuo Yoshinobu

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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.

Article information

Source
Tsukuba J. Math., Volume 36, Number 1 (2012), 53-66.

Dates
First available in Project Euclid: 10 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1341951744

Digital Object Identifier
doi:10.21099/tkbjm/1341951744

Mathematical Reviews number (MathSciNet)
MR2976549

Zentralblatt MATH identifier
1248.54015

Subjects
Primary: 54E35: Metric spaces, metrizability
Secondary: 03E17: Cardinal characteristics of the continuum 06A07: Combinatorics of partially ordered sets 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

Keywords
Smirnov compactification Stone-Čech compactification metrizable space generalized Galois-Tukey connection

Citation

Kada, Masaru; Yoshinobu, Yasuo. Galois-Tukey connection involving sets of metrics. Tsukuba J. Math. 36 (2012), no. 1, 53--66. doi:10.21099/tkbjm/1341951744. https://projecteuclid.org/euclid.tkbjm/1341951744


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