Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extending the Choquet theory: Trace convexity   We introduce the notion of trace convexity for functions and respectively,
for subsets of a compact topological space. This notion generalizes both
classical convexity of vector spaces, as well as Choquet convexity for compact
metric spaces. We provide new notions of trace-convexification for sets and
functions as well as a general version of Krein-Milman theorem. We show that
the class of upper semicontinuous convex-trace functions attaining their
maximum at exactly one Choquet-boundary point is residual and we obtain several
enhanced versions of the maximum principle which generalize both the classical
Bauer's theorem as well as its abstract version in the Choquet theory. We
illustrate our notions and results with concrete examples of three different
types.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg