Metrizable spaces where the inductive dimensions disagree

  title={Metrizable spaces where the inductive dimensions disagree},
  author={John Kulesza},
  journal={Transactions of the American Mathematical Society},
  • J. Kulesza
  • Published 1 February 1990
  • Mathematics
  • Transactions of the American Mathematical Society
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 N-compact, complete metrizable spaces with ind = 0 and Ind = 1 are provided, answering questions of Mrowka and Roy. An example with weight c and positive Ind such that subspaces with smaller weight have Ind = 0 is produced in ZFC. Assuming an additional axiom, for each cardinal A a space of… 
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