Metrizable spaces where the inductive dimensions disagree

Author:
John Kulesza

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

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Abstract | References | Similar Articles | Additional Information

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 -compact, complete metrizable spaces with and are provided, answering questions of Mrowka and Roy. An example with weight and positive Ind such that subspaces with smaller weight have is produced in ZFC. Assuming an additional axiom, for each cardinal a space of positive Ind with all subspaces with weight less than strongly zero-dimensional is constructed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0954600-9

Keywords:
Metrizable space,
full set,
dimension

Article copyright:
© Copyright 1990
American Mathematical Society