Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An equivalent condition for a uniform space to be coverable   We prove that an equivalent condition for a uniform space to be coverable is
that the images of the natural projections in the fundamental inverse system
are uniformly open in a certain sense. As corollaries we (1) obtain a concrete
way to find covering entourage, (2) correct an error in [3] and (3) show that
coverable is equivalent to chain connected and uniformly joinable in the sense
of arXiv:0706.3937.

30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph