Metrizable spaces where the inductive dimensions disagree

@article{Kulesza1990MetrizableSW,
  title={Metrizable spaces where the inductive dimensions disagree},
  author={John Kulesza},
  journal={Transactions of the American Mathematical Society},
  year={1990},
  volume={318},
  pages={763-781}
}
  • 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… 
New properties of Mrowka's space νμ0
We extend the technique of Mrowka to show that his space νμ 0 has the property that dim νμ n 0 = n while ind νμ n 0 = 0, assuming his extra set-theoretic hypothesis. We also show that νμ 0 is
Problems in perfect ordered spaces
In his landmark paper " Mappings and Spaces " [1966] A. V. Arkhangel-ski˘ ı introduced the class MOBI (Metric Open Bicompact Images) as the intersection of all classes of topological spaces
R-compact spaces with weight X < ExpRX
Answering a question of Arhangel’skii, we show – under GCH – that for most cardinals m there exists an R-compact space X such that weightX = m but X does not embed in a closed fashion into the
On strategies for selection games related to countable dimension
Two selection games from the literature, Gc(O,O) and G1(Ozd,O), are known to characterize countable dimension among certain spaces. This paper studies their perfectand limitedinformation strategies,
Small inductive dimension of completions of metric spaces. II
Extending the results of a previous paper under the same title we show that, under S(No), ind c vpe2 = 2.
...
1
2
...

References

SHOWING 1-10 OF 15 REFERENCES
NONEQUALITY OF DIMENSIONS FOR METRIC SPACES
and Ind (S) = n if Ind (S)^n but Ind (S)Sn-l is not true. Covering dimension (=Lebesgue covering dimension), denoted by dim such that dim (S) = 1 if S is empty, dim (S) S n if every finite open cover
Failure of equivalence of dimension concepts for metric spaces
Introduction. The three classical set-theoretic concepts of dimensions for topological spaces are [2, p. 153]: small inductive dimension —denoted by ind—such that ind (5) = — 1 if S is empty, ind(S)
On dimension theory
What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their
Set theoretic topology
  • University Microfilms International, Ann Arbor, Mich.
  • 1977
Prabir Roy's space A is not W-compact
  • General Topology Appl
  • 1973
Roy's space A is not W-compact
  • General Topology Appl
  • 1973
...
1
2
...