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 Banach algebras ${\rm C}(X, R)$ of continuous functions from acompact Hausdorff topological space $X$ to a Banach ring $R$ whose topology isdiscrete. We prove that the Berkovich spectrum of ${\rm C}(X, R)$ ishomeomorphic to $\zeta(X) \times {\mathcal M}(R)$, where $\zeta(X)$ is theBanaschewski compactification of $X$ and ${\mathcal M}(R)$ is the Berkovichspectrum of $R$. We study how the topology of the spectrum of ${\rm C}(X, R)$is related to the notion of homotopy Zariski open embedding used in derivedgeometry. We find that the topology of $\zeta(X)$ can be easily reconstructedfrom the homotopy Zariski topology associated to ${\rm C}(X, R)$. We also provesome results about the existence of Schauder bases on ${\rm C}(X, R)$ and ageneralisation of the Stone--Weierstrass Theorem, under suitable hypotheses on$X$ and $R$.

Derived Analytic Geometry for Z-Valued Functions. Part I -- Topological Properties