Quotients of countably based spaces are not closed under sobrification
نویسندگان
چکیده
In this note we show that quotients of countably based spaces (qcb spaces) and topological predomains as introduced by M. Schröder and A. Simpson are not closed under sobrification. As a consequence replete topological predomains need not be sober, i.e. in general repletion is not given by sobrification. Our counterexample also shows that a certain tentative “equalizer construction” of repletion fails for qcb spaces.
منابع مشابه
Topological predomains and qcb spaces are not closed under sobrification
In (Simpson 2003) A. Simpson introduced the category PreDom of topological predomains as a framework for denotational semantics containing also most classical spaces, namely all countably based T0 spaces. Countably based T0 spaces are isomorphic to subspaces of Pω where the latter is endowed with the Scott topology. A qcb space (as introduced in (Menni and Simpson 2002)) is a T0 space which app...
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ورودعنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 16 شماره
صفحات -
تاریخ انتشار 2006