Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of Sums of Subspace of Bounded Functions and Applications   We give a new proof of a characterization of the closeness of the range of a
continuous linear operator and of the closeness of the sum of two closed vector
subspaces of a Banach space. Then we state sufficient conditions for the
closeness of the sum of two closed subspaces of the Banach space of bounded
functions and apply this result on various pseudo almost periodic spaces and
pseudo almost automorphic spaces.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: math-ph