Copenhagen Programming Language Seminar


Quotients of countably based spaces are not closed under sobrification

Thomas Streicher,
Technische Universitšt Darmstadt

Wednesday, September 13th (!), 15:00-16:00
IT University of Copenhagen, Rued Langgaards Vej 7, Auditorium 3


Joint work between G. Gruenhage and T.Streicher

The notion of replete object was introduced by M. Hyland and P. Taylor around 1990 within Synthetic Domain Theory (SDT) in analogy with the sober spaces as known from topology. In this little note we show that for the realizability model over Scott's graph model and Kleene's function realizability model repletion is not given by sobrification. Thus there are replete objects which are not sober. Moreover, we show that a certain equalizer construction for repletion (as suggested by P.Taylor) fails to do its job.

Scientific host: Carsten Butz. Administrative host: Camilla Jensen. All are welcome.
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