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Proceedings of the American Mathematical Society
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Souslin's hypothesis and convergence in category

Author(s): Arnold W. Miller
Journal: Proc. Amer. Math. Soc. 124 (1996), 1529-1532.
MSC (1991): Primary 28A20; Secondary 03E65, 54E52
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Abstract: A sequence of functions $f_n\colon X\to\mathbb R$ from a Baire space $X$ to the reals $\mathbb R$ 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 converges in category converges everywhere on a comeager set. This answers a question of Wagner and Wilczynski who proved the converse.


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Additional Information:

Arnold W. Miller
Affiliation: University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
Email: miller@math.wisc.edu

DOI: 10.1090/S0002-9939-96-03409-0
PII: S 0002-9939(96)03409-0
Received by editor(s): November 2, 1994
Additional Notes: I want to thank Krzysztof Ciesielski for many helpful conversations
The results presented in this paper were obtained during the Joint US--Polish Workshop in Real Analysis, Lódz, Poland, July 1994. The workshop was partially supported by the NSF grant INT--9401673
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1996, American Mathematical Society


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