Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived Analytic Geometry for Z-Valued Functions. Part I -- Topological
  Properties   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 $R$.

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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex