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Probabilistic Powerdomains and Quasi-Continuous Domains

Abstract : The probabilistic powerdomain VX on a space X is the space of all continuous valuations on X. We show that, for every quasi-continuous domain X, VX is again a quasi-continuous domain, and that the Scott and weak topologies then agree on VX. This also applies to the subspaces of probability and subprobability valuations on X, in the first case under an assumption of pointedness. We also show that the Scott and weak topologies on VX may differ when X is not quasi-continuous, and we give a simple, compact Hausdorff counterexample.
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https://hal.archives-ouvertes.fr/hal-03260383
Contributor : Jean Goubault-Larrecq Connect in order to contact the contributor
Submitted on : Monday, June 14, 2021 - 8:17:39 PM
Last modification on : Tuesday, September 28, 2021 - 1:53:42 PM
Long-term archiving on: : Thursday, September 16, 2021 - 8:26:30 AM

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  • HAL Id : hal-03260383, version 1

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Jean Goubault-Larrecq. Probabilistic Powerdomains and Quasi-Continuous Domains. Topology Proceedings, Auburn University Mathematics Dept., 2022, 60, pp.1-16. ⟨hal-03260383⟩

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