Probabilistic Powerdomains and Quasi-Continuous Domains

zbMath1498.54032arXiv2007.04189MaRDI QIDQ5095209

Jean Goubault-Larrecq

Publication date: 5 August 2022

Abstract: The probabilistic powerdomain $mathbfVX$ on a space $X$ is the space of all continuous valuations on $X$. We show that, for every quasi-continuous domain $X$, $mathbfVX$ is again a quasi-continuous domain, and that the Scott and weak topologies then agree on $mathbfVX$. This also applies to the subspaces of probability and subprobability valuations on $X$. We also show that the Scott and weak topologies on the $mathbfVX$ may differ when $X$ is not quasi-continuous, and we give a simple, compact Hausdorff counterexample.

Full work available at URL: https://arxiv.org/abs/2007.04189

zbMATH Keywords

weak topologyScott topologyprobabilistic powerdomainquasi-continuous domainlocally finitary compact space

Mathematics Subject Classification ID

Miscellaneous topics in measure theory (28E99) Peculiar topological spaces (54G99)

Cites Work

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Related Items (1)

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