Szpilrajn type theorem for concentration dimension (Q2773374)
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scientific article; zbMATH DE number 1709964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Szpilrajn type theorem for concentration dimension |
scientific article; zbMATH DE number 1709964 |
Statements
Szpilrajn type theorem for concentration dimension (English)
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21 February 2002
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Hausdorff dimension
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topological dimension
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Lévy concentration function
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concentration dimension
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locally compact separable metric space
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Let \(X\) be a locally compact separable metric space. It is proved that NEWLINE\[NEWLINE\dim_T(X) =\inf\{\dim_LX': X'\text{ is homeomorphic to }X\},NEWLINE\]NEWLINE where \(\dim_L(X)\) and \(\dim_T(X)\) stand for the concentration dimension and the topological dimension of \(X\), respectively.
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