Failure of equivalence of dimension concepts for metric spaces

@article{Roy1962FailureOE,
  title={Failure of equivalence of dimension concepts for metric spaces},
  author={Prabir Roy},
  journal={Bulletin of the American Mathematical Society},
  year={1962},
  volume={68},
  pages={609-613}
}
  • P. Roy
  • Published 1 November 1962
  • Mathematics
  • Bulletin of the American Mathematical Society
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) ^ n if for every point p £ S and open set U containing p there is an open set F with pG VC Uand ind(bdry V)^n-1, and ind(5) = n if ind(5) Sn but ind(5) l^n — 1 is not true; large inductive dimension—denoted by Ind—such that I n d ( 5 ) = — 1 if 5 is empty, I nd (5 )^w if for every closed set C and… 
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