# 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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