Keimel, Klaus - Weak upper topologies and duality for cones

lmcs:1597 - Logical Methods in Computer Science, September 25, 2015, Volume 11, Issue 3
Weak upper topologies and duality for cones

Authors: Keimel, Klaus

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.

Source :
DOI : 10.2168/LMCS-11(3:21)2015
Volume: Volume 11, Issue 3
Published on: September 25, 2015
Submitted on: May 16, 2013
Keywords: Computer Science - Logic in Computer Science


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