A Universal Continuum of Weight ℵ
نویسنده
چکیده
We prove that every continuum of weight ℵ 1 is a continuous image of thě Cech-Stone-remainder R * of the real line. It follows that under CH the remainder of the half line [0, ∞) is universal among the continua of weight c — universal in the 'mapping onto' sense. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R * , 2) in the Cohen model the long segment of length ω 2 + 1 is not a continuous image of R * , and 3) PFA implies that Iu is not a continuous image of R * , whenever u is a c-saturated ultrafilter. We also show that a universal continuum can be gotten from a c-saturated ultrafilter on ω and that it is consistent that there is no universal continuum of weight c.
منابع مشابه
A Universal Continuum of Weight ℵ
We prove that every continuum of weight א1 is a continuous image of the Čech-Stone-remainder R of the real line. It follows that under CH the remainder of the half line [0,∞) is universal among the continua of weight c. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R, 2) in the Cohen model the long segment of length ω2 + 1 i...
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