Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The order versions of the Hahn--Banach Theorem and envelopes. I.
  Homogeneous functions   We present here the General formulation of the problem of existence and
construction of upper and lower envelope for an arbitrary function with values
from the completion of the ordered set ${\rm S}$ for a certain class of
functions with values in ${\rm S}$. The task is parsed only for the simplest
case of model class of homogeneous functions. Consider only order-algebraic
version without the involvement of the topology.

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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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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: nucl-th
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The categories of this paper are: adap-org