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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Souslin's hypothesis and convergence in category


Author: Arnold W. Miller
Journal: Proc. Amer. Math. Soc. 124 (1996), 1529-1532
MSC (1991): Primary 28A20; Secondary 03E65, 54E52
MathSciNet review: 1328364
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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: http://dx.doi.org/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, Łódź, Poland, July 1994. The workshop was partially supported by the NSF grant INT–9401673
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society