Abstract
AbstractIn 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 ω1.
Publisher
Cambridge University Press (CUP)
Reference10 articles.
1. Sur un ensemble non dénombrable donte toute image continue est de mesure null;Sierpinski;Fundamenta Mathematical,1928
2. On the consistency of Borel's conjecture
3. On a proposition of Sierpinski's which is equivalent to the continuum hypothesis;Bagemihl;Proceedings of the American Mathematical Society,1954
4. Spaces without Large Projective Subspaces.
Cited by
48 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献