A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 247-255
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Let $X$ be a Polish space. We will prove that $${{\dim}_{T}}X=\inf \left\{ {{\dim}_{L}}{X}'\,:\,{X}'\,\text{is homeomorphic to }X\, \right\},$$ where ${{\dim}_{L}}\,X$ and ${{\dim}_{T}}\,X$ stand for the concentration dimension and the topological dimension of $X$ , respectively.
Mots-clés :
11K55, 28A78, Hausdorff dimension, topological dimension, Lévy concentration function, concentration dimension
Myjak, Józef; Szarek, Tomasz; Śleçzka, Maciej. A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 247-255. doi: 10.4153/CMB-2006-025-1
@article{10_4153_CMB_2006_025_1,
author = {Myjak, J\'ozef and Szarek, Tomasz and \'Sle\c{c}zka, Maciej},
title = {A {Szpilrajn{\textendash}Marczewski} {Type} {Theorem} for {Concentration} {Dimension} on {Polish} {Space}},
journal = {Canadian mathematical bulletin},
pages = {247--255},
year = {2006},
volume = {49},
number = {2},
doi = {10.4153/CMB-2006-025-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-025-1/}
}
TY - JOUR AU - Myjak, Józef AU - Szarek, Tomasz AU - Śleçzka, Maciej TI - A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space JO - Canadian mathematical bulletin PY - 2006 SP - 247 EP - 255 VL - 49 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-025-1/ DO - 10.4153/CMB-2006-025-1 ID - 10_4153_CMB_2006_025_1 ER -
%0 Journal Article %A Myjak, Józef %A Szarek, Tomasz %A Śleçzka, Maciej %T A Szpilrajn–Marczewski Type Theorem for Concentration Dimension on Polish Space %J Canadian mathematical bulletin %D 2006 %P 247-255 %V 49 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-025-1/ %R 10.4153/CMB-2006-025-1 %F 10_4153_CMB_2006_025_1
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