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I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension \alpha$\alpha$.
Then for any \beta < \alpha$\beta < \alpha$,
X contains a closed subset whose Hausdorff dimension is \beta$\beta$.
I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension \alpha.
Then for any \beta < \alpha,
X contains a closed subset whose Hausdorff dimension is \beta.
I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension $\alpha$.
Then for any $\beta < \alpha$,
X contains a closed subset whose Hausdorff dimension is $\beta$.
