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

We study the class of overconvergent subanalytic subsets of a $k$-affinoidspace $X$ when $k$ is a non-archimedean field. These are the images along theprojection $X \times B^n \to X$ of subsets defined with inequalities betweenfunctions of $X\times B^n$ which are overconvergent in the variables of $B^n$.In particular, we study the local nature, with respect to $X$, ofoverconvergent subanalytic subsets. We show that they behave well with respectto the Berkovich topology, but not to the $G$-topology. This givescounter-examples to previous results on the subject, and a way to correct them.Moreover, we study the case dim$(X)=2$, for which a simpler characterisation ofoverconvergent subanalytic subsets is proven.

Overconvergent subanalytic subsets in the framework of Berkovich spaces