2004/12/31 by Masaru Kada, Kada, Masaru, Kazuo Tomoyasu +3
Mathematics · #03E17 #54D35 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #math.GN #msc:03E17 #msc:54D35
paper · pdf · doi:10.48550/arxiv.math/0412547
V2: minor linguistic corrections
openalex publication_date 2004/12/31 · arxiv created 2006/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the Stone-Cech compactification of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a set D of compatible metrics on X such that the Stone-Cech compactification of X is approximated by Smirnov or Higson compactifications for all metrics in D. We prove that it is either the dominating number or 1 for a locally compact separable metrizable space.