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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 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.
References:
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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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