Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hawaiian earring group is topologically incomplete   The premier exhibition of the following phenomenon: The fundamental group of
any Peano continuum constructed in similar fashion to the Hawaiian earring
admits two natural distinct topological group structures. However despite being
uncountable and regular, neither group is a Baire space and hence neither group
admits a compatible complete metric.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg