Souslin's Hypothesis and Convergence in Category

Arnold W. Miller

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Souslin's Hypothesis and Convergence in Category

Arnold W. Miller

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Abstract

A sequence of functions f_n: X -> R from a Baire space X to the reals is said to converge in category iff every subsequence has a subsequence which converges on all but a meager set. We show that if there exists a Souslin Tree then there exists a nonatomic Baire space X such that every sequence which converge in category converges everywhere on a comeager set. This answers a question of Wagner and Wilczynski, Convergence of sequences of measurable functions, Acta Math Acad Sci Hung 36(1980), 125-128.

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BibTeX RIS

Arnold W. Miller. 1994-11-01. Souslin's Hypothesis and Convergence in Category. https://arxiv.org/abs/math/9411205

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