Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A topological group observation on the Banach--Mazur separable quotient
  problem   The Banach-Mazur problem, which asks if every infinite-dimensional Banach
space has an infinite-dimensional separable quotient space, has remained
unsolved for 85 years, but has been answered in the affirmative for special
cases such as reflexive Banach spaces. It is also known that every
infinite-dimensional non-normable Fr\'{e}chet space has an infinite-dimensional
separable quotient space, namely $\mathbb{R}^\omega $. It is proved in this
paper that every infinite-dimensional Fr\'{e}chet space (including every
infinite-dimensional Banach space), indeed every locally convex space which has
a subspace which is an infinite-dimensional Fr\'{e}chet space, has an
infinite-dimensional (in the topological sense) separable metrizable quotient
group, namely $\mathbb{T}^\omega$, where $\mathbb{T}$ denotes the compact unit
circle group.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin