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Jung-Tix problem in sober dcpos

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If you have a question about this talk, please contact Uday Reddy.

Jung-Tix problem asks for a cartesian closed category of continuous domains that is simultaneously closed under Jones’ probabilistic monad. We are going to see that all cartesian closed categories of quasicontinuous domains consist of continuous domains, and this entails that the Jung-Tix problem in quasicontinuous domains is of the same difficulty as in continuous domains.

We will also consider this question topologically, and try to find potential solutions in locally compact sober pointed dcpos, and our results will lead us to the category of stably compact dcpos. Alongside, some interesting results of coherence will be revealed.

This talk is part of the Lab Lunch series.

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