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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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Authors: Alan Dow and Stephen Watson
Journal: Trans. Amer. Math. Soc. 337 (1993), 825-837
MSC: Primary 54A35; Secondary 18B30, 54B30
MathSciNet review: 1097165
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Abstract: We consider the smallest class of topological spaces which contains the converging sequence and which is closed under the operations of taking arbitrary sums, quotients and finite products. We show that if there is a model of set-theory in which there is a measurable cardinal then there is a model in which this class does not contain all topological spaces. In addition, we prove that it is consistent that this class does contain all topological spaces--in fact much more, a large cardinal is needed to produce a model of set theory in which this class is proper.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1097165-9
PII: S 0002-9947(1993)1097165-9
Article copyright: © Copyright 1993 American Mathematical Society