Journal of Symbolic Logic 48 (3):575-584 (1983)

Abstract
In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1
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DOI 10.2307/2273449
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References found in this work BETA

Iterated Perfect-Set Forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.

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A Model with No Magic Set.Krzysztof Ciesielski & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (4):1467-1490.

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