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**1 - 3**of**3**### Under consideration for publication in Math. Struct. in Comp. Science Quotients of countably based spaces are not

, 2006

"... Dedicated to Klaus Keimel on the occasion of his 65th birthday 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 no ..."

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Dedicated to Klaus Keimel on the occasion of his 65th birthday 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. Our results extend also to the more general class of core compactly generated spaces.