Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The set of bounded continuous nowhere locally uniformly continuous
  functions is not Borel   It is known that for $X$ a nowhere locally compact metric space, the set of
bounded continuous, nowhere locally uniformly continuous real-valued functions
on $X$ contains a dense $G_\delta$ set in the space $C_b(X)$ of all bounded
continuous real-valued functions on $X$ in the supremum norm. Furthermore, when
$X$ is separable, the set of bounded continuous, nowhere locally uniformly
continuous real-valued functions on $X$ is itself a $G_\delta$ set. We show
that in contrast, when $X$ is nonseparable, this set of functions is not even a
Borel set.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess