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

DOI:
https://doi.org/10.1090/S0002-9939-96-03409-0

MathSciNet review:
1328364

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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence of functions from a Baire space 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 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:
https://doi.org/10.1090/S0002-9939-96-03409-0

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