Spaces of Valuations

  title={Spaces of Valuations},
  author={R. Heckmann},
  journal={Annals of the New York Academy of Sciences},
  • R. Heckmann
  • Published 1996
  • Biology
  • Annals of the New York Academy of Sciences
  • 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… CONTINUE READING
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