Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Achievement sets and sum ranges with ideal supports   We introduce the notion of ideally supported achievement sets for a series of
real numbers. We analize their complexity and topological properties. We
compare the notion of ideal achievement sets with the notion of ideally
supported sum range of real series, considered by Filip\'ow and Szuca. We
complete Filip\'ow and Szuca characterization of ideal sum ranges, [R.
Filip\'ow, P. Szuca, Rearrangement of conditionally convergent series on a
small set, J. Math. Anal. Appl. 362 (2010), no. 1, 64-71.], and we obtain some
generalization of Riemann's Theorem.

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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin