Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly Circle-Preserving Maps in Inversive Geometry   Let S^n be the standard n-sphere embedded in R^{n+1}. A mapping T: S^n \to
S^n, not assumed continuous or even measurable, nor injective, is called weakly
circle-preserving if the image of any circle under T is contained in some
circle in the range space S^n. The main result of this paper shows that any
weakly circle-preserving map satisfying a very mild condition on its range
T(S^n) must be a Mobius transformation.

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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex