Geodesic
Szpilrajn type theorem for concentration dimension
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
Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 19-25 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm172-1-2
Mots-clés : locally compact separable metric space prove dim inf dim hbox homeomorphic where dim dim stand concentration dimension topological dimension respectively

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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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

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