Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on vanishing geodesic distances in infinite dimensions   We observe that a vanishing geodesic distance arising from a weak Riemannian
metric in a Hilbert manifold can be constructed.

32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys