Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximately Vanishing of Topological Cohomology Groups   In this paper, we establish the Pexiderized stability of coboundaries and
cocycles and use them to investigate the Hyers--Ulam stability of some
functional equations. We prove that for each Banach algebra $A$, Banach
$A$-bimodule $X$ and positive integer $n, H^n(A,X)=0$ if and only if the $n$-th
cohomology group approximately vanishes.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th