Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary Relations in Mathematical Economics: On the Continuity,
  Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot   This chapter examines how positivity and order play out in two important
questions in mathematical economics, and in so doing, subjects the postulates
of continuity, additivity and monotonicity to closer scrutiny. Two sets of
results are offered: the first departs from Eilenberg's (1941) necessary and
sufficient conditions on the topology under which an anti-symmetric, complete,
transitive and continuous binary relation exists on a topologically connected
space; and the second, from DeGroot's (1970) result concerning an additivity
postulate that ensures a complete binary relation on a {\sigma}-algebra to be
transitive. These results are framed in the registers of order, topology,
algebra and measure-theory; and also beyond mathematics in economics: the
exploitation of Villegas' notion of monotonic continuity by Arrow-Chichilnisky
in the context of Savage's theorem in decision theory, and the extension of
Diamond's impossibility result in social choice theory by Basu-Mitra. As such,
this chapter has a synthetic and expository motivation, and can be read as a
plea for inter-disciplinary conversations, connections and collaboration.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys