English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $R$ be an o-minimal expansion of the real field. We show that theHausdorff dimension of an $R$-definable metric space is an $R$-definablefunction of the parameters defining the metric space. We also show that theHausdorff dimension of an $R$-definable metric space is an element of the fieldof powers of $R$. The proof uses a basic topological dichotomy for definablemetric spaces due to the second author, and the work of the first author andShiota on measure theory over nonarchimedean o-minimal structures.

The Hausdorff dimension of metric spaces definable in o-minimal expansions of the real field