Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Choice free Fixed Point Property in separable Banach spaces   We show that the standard approach of minimal invariant sets, which applies
Zorn's Lemma and is used to prove fixed point theorems for non-expansive
mappings in Banach spaces can be applied without any reference to the full
Axiom of Choice when the given Banach space is separable. Our method applies
results from classical and effective descriptive set theory.

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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph