Metrizable spaces where the inductive dimensions disagree
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- by John Kulesza PDF
- Trans. Amer. Math. Soc. 318 (1990), 763-781 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 318 (1990), 763-781
- MSC: Primary 54F45
- DOI: https://doi.org/10.1090/S0002-9947-1990-0954600-9
- MathSciNet review: 954600