1Dipartimento di Matematica Pura ed Applicata Università di L'Aquila Via Vetoio 67100 L'Aquila, Italy and WSM AGH Mickiewicza 30 30-059 Kraków, Poland 2Institute 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
Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 19-25
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.
Mots-clés :
locally compact separable metric space prove dim inf dim hbox homeomorphic where dim dim stand concentration dimension topological dimension respectively
Affiliations des auteurs :
Jozef Myjak
1
;
Tomasz Szarek
2
1
Dipartimento di Matematica Pura ed Applicata Università di L'Aquila Via Vetoio 67100 L'Aquila, Italy and WSM AGH Mickiewicza 30 30-059 Kraków, Poland
2
Institute 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
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author = {Jozef Myjak and Tomasz Szarek},
title = {Szpilrajn type theorem for concentration dimension},
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Jozef Myjak; Tomasz Szarek. Szpilrajn type theorem for concentration dimension. Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 19-25. doi: 10.4064/fm172-1-2
