Szpilrajn type theorem for concentration dimension

Volume 172 / 2002

Jozef Myjak, Tomasz Szarek Fundamenta Mathematicae 172 (2002), 19-25 MSC: Primary 11K55; Secondary 28A78. DOI: 10.4064/fm172-1-2

Abstract

Let $X$ be a locally compact, separable metric space. We prove that $\dim_{\rm T} X=\inf \{\dim_{\rm L} X': X'\hbox{ is homeomorphic to } X\}$, where $\dim_{\rm L} X$ and $\dim_{\rm T} X$ stand for the concentration dimension and the topological dimension of $X$, respectively.

Authors

  • Jozef MyjakDipartimento di Matematica Pura ed Applicata
    Università di L'Aquila
    Via Vetoio
    67100 L'Aquila, Italy
    and
    WSM AGH
    Mickiewicza 30
    30-059 Kraków, Poland
    e-mail
  • Tomasz SzarekInstitute of Mathematics
    Polish Academy of Sciences
    Bankowa 14
    40-007 Katowice, Poland
    and
    Department of Mathematics
    Technical University of Rzeszów
    Pola 6
    35-959 Rzeszów, Poland
    e-mail

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