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- W3184867722 abstract "We study the Banach algebras ${rm C}(X, R)$ of continuous functions from a compact Hausdorff topological space $X$ to a Banach ring $R$ whose topology is discrete. We prove that the Berkovich spectrum of ${rm C}(X, R)$ is homeomorphic to $zeta(X) times {mathcal M}(R)$, where $zeta(X)$ is the Banaschewski compactification of $X$ and ${mathcal M}(R)$ is the Berkovich spectrum 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 derived geometry. We find that the topology of $zeta(X)$ can be easily reconstructed from the homotopy Zariski topology associated to ${rm C}(X, R)$. We also prove some results about the existence of Schauder bases on ${rm C}(X, R)$ and a generalisation of the Stone--Weierstrass Theorem, under suitable hypotheses on $X$ and $R$." @default.
- W3184867722 created "2021-08-02" @default.
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- W3184867722 date "2021-07-19" @default.
- W3184867722 modified "2023-09-26" @default.
- W3184867722 title "Derived Analytic Geometry for Z-Valued Functions. Part I -- Topological Properties" @default.
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- W3184867722 doi "https://doi.org/10.48550/arxiv.2107.09004" @default.
- W3184867722 hasPublicationYear "2021" @default.
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