2004/05/16 by Masaru Kada, Kada, Masaru, Kazuo Tomoyasu +3
Computer Science · Mathematics · #03E17 #03E35 #54D35 #54H05 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:03E17 #msc:03E35 #msc:54D35 #msc:54H05
paper · pdf · doi:10.48550/arxiv.math/0405311
v3: Unified old sections 1 and 2 into new section 1, and deleted some basic lemmata to shorten the article
openalex publication_date 2004/05/16 · arxiv created 2004/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the Stone-Čech compactification of a non-compact metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. We investigate the smallest cardinality of a set D of compatible metrics on the countable discrete space ω such that, the Stone-Čech compactification of ω is approximated by Smirnov compactifications for all metrics in D, but any finite subset of D does not suffice. We also study the corresponding cardinality for Higson compactifications.