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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Metrizable spaces where the inductive dimensions disagree

Author: John Kulesza
Journal: Trans. Amer. Math. Soc. 318 (1990), 763-781
MSC: Primary 54F45
MathSciNet review: 954600
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Abstract: A method for constructing zero-dimensional metrizable spaces is given. Using generalizations of Roy's technique, these spaces can often be shown to have positive large inductive dimension. Examples of $ {\mathbf{N}}$-compact, complete metrizable spaces with $ \operatorname{ind} = 0$ and $ \operatorname{Ind} = 1$ are provided, answering questions of Mrowka and Roy. An example with weight $ \mathfrak{c}$ and positive Ind such that subspaces with smaller weight have $ \operatorname{Ind} = 0$ is produced in ZFC. Assuming an additional axiom, for each cardinal $ \lambda $ a space of positive Ind with all subspaces with weight less than $ \lambda $ strongly zero-dimensional is constructed.

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Keywords: Metrizable space, full set, dimension
Article copyright: © Copyright 1990 American Mathematical Society

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