Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Transcendental Fields   This article initiates the study of topological transcendental fields $\FF$
which are subfields of the topological field $\CC$ of all complex numbers such
that $\FF$ consists of only rational numbers and a nonempty set of
transcendental numbers. $\FF$, with the topology it inherits as a subspace of
$\CC$, is a topological field. Each topological transcendental field is a
separable metrizable zero-dimensional space and algebraically is $\QQ(T)$, the
extension of the field of rational numbers by a set $T$ of transcendental
numbers. It is proved that there exist precisely $2^{\aleph_0}$ countably
infinite topological transcendental fields and each is homeomorphic to the
space $\QQ$ of rational numbers with its usual topology. It is also shown that
there is a class of $2^{2^{\aleph_0} }$ of topological transcendental fields of
the form $\QQ(T)$ with $T$ a set of Liouville numbers, no two of which are
homeomorphic.

27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol