Abstract
It is known that for each continuous image of N⁎, there is a nowhere dense weak P-set of N⁎ that maps irreducibly onto it. We generalize this for every compact space of weight at most c. This allows us to show that there is a weak P-set in N⁎ which is homeomorphic to N⁎. This generalizes a result of the first-named author and answers a problem posed before 1990.
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