Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak upper topologies and duality for cones   In functional analysis it is well known that every linear functional defined
on the dual of a locally convex vector space which is continuous for the weak
topology is the evaluation at a uniquely determined point of the given vector
space. M. Schroeder and A. Simpson have obtained a similar result for lower
semicontinuous linear functionals on the cone of all Scott-continuous
valuations on a topological space endowed with the weak upper topology, an
asymmetric version of the weak topology. This result has given rise to several
proofs, originally by the Schroeder and Simpson themselves and, more recently,
by the author of these Notes and by J. Goubault-Larrecq. The proofs developed
from very technical arguments to more and more conceptual ones. The present
Note continues on this line, presenting a conceptual approach inspired by
classical functional analysis which may prove useful in other situations.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc