Abstract
ABSTRACT:Valuations are measurelike functions mapping the open sets of a topological space X into positive real numbers. They can be classified into finite, point continuous, and Scott continuous valuations. We define corresponding spaces of valuations VfX⊂ VpX⊂VX. The main results of the paper are that VpX is the soberification of VfX, and that VpX is the free sober locally convex topological cone over X. From this universal property, the notion of the integral of a real‐valued function over a Scott continuous valuation can be easily derived. The integral is used to characterize the spaces VpX and VX as dual spaces of certain spaces of real‐valued functions on X.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
