A subcategory of TOP

Dow, Alan; Watson, Stephen

doi:10.1090/S0002-9947-1993-1097165-9

A subcategory of TOP

Authors: Alan Dow and Stephen Watson
Journal: Trans. Amer. Math. Soc. 337 (1993), 825-837
MSC: Primary 54A35; Secondary 18B30, 54B30
DOI: https://doi.org/10.1090/S0002-9947-1993-1097165-9
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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