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A Quasicontinuous Domain Without an Interval Retract
We give negative answers to two questions of X.Xu concerning the occurrence of the unit interval in nonquasialgebraic quasicontinuous domains. We construct, directly from the binary tree and the binary-value map, a well-founded quasicontinuous dcpo \[ P=2^{<ω}\mathbin{\dot\cup}[0,1] \] which is not
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