Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a characterization of path connected topological fields   The aim of this paper is to give a characterization of path connected
topological fields, inspired by the classical Gelfand correspondence between a
compact Hausdorff topological space $X$ and the space of maximal ideals of the
ring of real valued continuous functions $C(X,\mathbb{R})$. More explicitly,
our motivation is the following question: What is the essential property of the
topological field $F=\mathbb{R}$ that makes such a correspondence valid for all
compact Hausdorff spaces? It turns out that such a perfect correspondence
exists if and only if $F$ is a path connected topological field.

26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph