Base normal inductive dimension $\mathrm I$ of cubes

A. V. Karassev^a, K. L. Kozlov<sup>b

a</sup> Nipissing University, Canada
^b Lomonosov Moscow State University

Abstract: It is shown that $\{1,\infty\}$ is the set of possible base normal inductive dimensions $\mathrm I$ of the segment $I=[0,1]$ and $\{n,n+1,\dots,\infty\}$ is the set of possible base normal inductive dimensions $\mathrm I$ of the $n$-dimensional cubes $I^n$ for $n\geq2$.

UDC: 515.127

 English version: Journal of Mathematical Sciences (New York), 2017, 223:6, 725–733

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